Volume 139, Issue 16, 28 October 2013

In this work, we validate a new, fully analytical method for calculating Raman intensities of periodic systems, developed and presented in Paper I [L. Maschio, B. Kirtman, M. Rérat, R. Orlando, and R. Dovesi, J. Chem. Phys.139, 164101 (2013)]. Our validation of this method and its implementation in the CRYSTAL code is done through several internal checks as well as comparison with experiment. The internal checks include consistency of results when increasing the number of periodic directions (from 0D to 1D, 2D, 3D), comparison with numerical differentiation, and a test of the sum rule for derivatives of the polarizability tensor. The choice of basis set as well as the Hamiltonian is also studied. Simulated Raman spectra of αquartz and of the UiO66 MetalOrganic Framework are compared with the experimental data.
 ARTICLES

 Theoretical Methods and Algorithms

Ab initio analytical Raman intensities for periodic systems through a coupled perturbed HartreeFock/KohnSham method in an atomic orbital basis. I. Theory
View Description Hide DescriptionWe present a fully analytical formulation for calculating Raman intensities of crystalline periodic systems using a local basis set. Numerical differentiation with respect to atomic coordinates and with respect to wavevectors is entirely avoided as is the determination of crystal orbital coefficient derivatives with respect to nuclear displacements. Instead, our method utilizes the orbital energyweighted density matrix and is based on the selfconsistent solution of first and secondorder Coupled Perturbed HartreeFock/KohnSham equations for the electronic response to external electric fields at the equilibrium geometry. This method has also been implemented in the CRYSTAL program, which uses a Gaussian type basis set.

Ab initio analytical Raman intensities for periodic systems through a coupled perturbed HartreeFock/KohnSham method in an atomic orbital basis. II. Validation and comparison with experiments
View Description Hide DescriptionIn this work, we validate a new, fully analytical method for calculating Raman intensities of periodic systems, developed and presented in Paper I [L. Maschio, B. Kirtman, M. Rérat, R. Orlando, and R. Dovesi, J. Chem. Phys.139, 164101 (2013)]. Our validation of this method and its implementation in the CRYSTAL code is done through several internal checks as well as comparison with experiment. The internal checks include consistency of results when increasing the number of periodic directions (from 0D to 1D, 2D, 3D), comparison with numerical differentiation, and a test of the sum rule for derivatives of the polarizability tensor. The choice of basis set as well as the Hamiltonian is also studied. Simulated Raman spectra of αquartz and of the UiO66 MetalOrganic Framework are compared with the experimental data.

SubOhmic spinboson model with offdiagonal coupling: Ground state properties
View Description Hide DescriptionWe have carried out analytical and numerical studies of the spinboson model in the subohmic regime with the influence of both the diagonal and the offdiagonal coupling accounted for, via the Davydov D1 variational ansatz. While a secondorder phase transition is known to be exhibited by this model in the presence of diagonal coupling only, we demonstrate the emergence of a discontinuous first order phase transition upon incorporation of the offdiagonal coupling. A plot of the ground state energy versus magnetization highlights the discontinuous nature of the transition between the isotropic (zero magnetization) state and nematic (finite magnetization) phases. We have also calculated the entanglement entropy and a discontinuity found at a critical coupling strength further supports the discontinuous crossover in the spinboson model in the presence of offdiagonal coupling. It is further revealed via a canonical transformation approach that for the special case of identical exponents for the spectral densities of the diagonal and the offdiagonal coupling, there exists a continuous crossover from a single localized phase to doubly degenerate localized phase with differing magnetizations.

Application of recent doublehybrid density functionals to lowlying singletsinglet excitation energies of large organic compounds
View Description Hide DescriptionThe present work assesses some recently developed doublehybrid density functionals (B2πPLYP, PBE0DH, and PBE02) using linearresponse TammDancoff TimeDependent Density Functional Theory. This assessment is achieved against experimentally derived lowlying excitation energies of large organic dyes of recent interest, including some excitations dominated by chargetransfer transitions. Comparisons are made with some of the bestperforming methods established from the literature, such as PBE0 or B3LYP hybrid or the recently proposed B2PLYP and B2GPPLYP doublehybrid models, to ascertain their quality and robustness on equal footing. The accuracy of parameterfree or empirical forms of doublehybrid functionals is also briefly discussed. Generally speaking, it turns out that doublehybrid expressions always provide more accurate estimates than corresponding hybrid methods. Doublehybrid functionals actually reach averaged accuracies of 0.2 eV, that can be admittedly considered close to any intended accuracy limit within the present theoretical framework.

Neural networks for local structure detection in polymorphic systems
View Description Hide DescriptionThe accurate identification and classification of local ordered and disordered structures is an important task in atomistic computer simulations. Here, we demonstrate that properly trained artificial neural networks can be used for this purpose. Based on a neural network approach recently developed for the calculation of energies and forces, the proposed method recognizes local atomic arrangements from a set of symmetry functions that characterize the environment around a given atom. The algorithm is simple and flexible and it does not rely on the definition of a reference frame. Using the LennardJones system as well as liquid water and ice as illustrative examples, we show that the neural networks developed here detect amorphous and crystalline structures with high accuracy even in the case of complex atomic arrangements, for which conventional structure detection approaches are unreliable.

Accurate and efficient integration for molecular dynamics simulations at constant temperature and pressure
View Description Hide DescriptionIn molecular dynamics simulations, control over temperature and pressure is typically achieved by augmenting the original system with additional dynamical variables to create a thermostat and a barostat, respectively. These variables generally evolve on timescales much longer than those of particle motion, but typical integrator implementations update the additional variables along with the particle positions and momenta at each time step. We present a framework that replaces the traditional integration procedure with separate barostat, thermostat, and Newtonian particle motion updates, allowing thermostat and barostat updates to be applied infrequently. Such infrequent updates provide a particularly substantial performance advantage for simulations parallelized across many computer processors, because thermostat and barostat updates typically require communication among all processors. Infrequent updates can also improve accuracy by alleviating certain sources of error associated with limitedprecision arithmetic. In addition, separating the barostat, thermostat, and particle motion update steps reduces certain truncation errors, bringing the timeaverage pressure closer to its target value. Finally, this framework, which we have implemented on both generalpurpose and specialpurpose hardware, reduces software complexity and improves software modularity.

Extension of the nonMarkovian EnergyCorrected Sudden model to the case of parallel and perpendicular infrared bands
View Description Hide DescriptionThe nonMarkovian EnergyCorrected Sudden approach [J. Buldyreva and L. Bonamy, Phys. Rev. A60, 370 (1999)] previously developed for wideband rototranslational Raman spectra of linear rotors is extended to the case of infrared absorption by linear molecules with stretching and bending modes. Basic relations such as detailed balance and doublesided sum rules for the rotational relaxation matrix are easily satisfied owing to the specific choice of a symmetric metric in the Liouville space. A single set of model parameters deduced from experimental widths of isolated isotropic Raman lines enables calculations of lineshape characteristics and full spectra up to the far wings. Applications to the important but quite complex example of pure carbon dioxide indicate the crucial role of the frequency dependence in the relaxation operator even for calculations of isolatedline characteristics.

Control of Turing patterns and their usage as sensors, memory arrays, and logic gates
View Description Hide DescriptionWe study a model system of three diffusively coupled reaction cells arranged in a linear array that display Turing patterns with special focus on the case of equal coupling strength for all components. As a suitable model reaction we consider a twovariable core model of glycolysis. Using numerical continuation and bifurcation techniques we analyze the dependence of the system's steady states on varying rate coefficient of the recycling step while the coupling coefficients of the inhibitor and activator are fixed and set at the ratios 100:1, 1:1, and 4:5. We show that stable Turing patterns occur at all three ratios but, as expected, spontaneous transition from the spatially uniform steady state to the spatially nonuniform Turing patterns occurs only in the first case. The other two cases possess multiple Turing patterns, which are stabilized by secondary bifurcations and coexist with stable uniform periodic oscillations. For the 1:1 ratio we examine modular spatiotemporal perturbations, which allow for controllable switching between the uniform oscillations and various Turing patterns. Such modular perturbations are then used to construct chemical computing devices utilizing the multiple Turing patterns. By classifying various responses we propose: (a) a singleinput resettable sensor capable of reading certain value of concentration, (b) twoinput and threeinput memory arrays capable of storing logic information, (c) threeinput, threeoutput logic gates performing combinations of logical functions OR, XOR, AND, and NAND.

Ndensity representability and the optimal transport limit of the HohenbergKohn functional
View Description Hide DescriptionWe derive and analyze a hierarchy of approximations to the strongly correlated limit of the HohenbergKohn functional. These “density representability approximations” are obtained by first noting that in the strongly correlated limit, Nrepresentability of the pair density reduces to the requirement that the pair density must come from a symmetric Npoint density. One then relaxes this requirement to the existence of a representing symmetric kpoint density with k < N. The approximate energy can be computed by simulating a fictitious kelectron system. We investigate the approximations by deriving analytically exact results for a 2site model problem, and by incorporating them into a selfconsistent KohnSham calculation for small atoms. We find that the low order representability conditions already capture the main part of the correlations.

Variationally localized search direction method for constrained optimization of nonorthogonal, localized orbitals in electronic structure calculations
View Description Hide DescriptionA new method for the constrained optimization of nonorthogonal, spatially localized orbitals using direct energy minimization techniques, in the context of electronic structure calculations, is presented. The variationally localized search direction (VLSD) method, as it was named, ensures that strict localization constraints are imposed upon the search direction vectors exactly, analytically and in a fully variational fashion. In contrast, the truncated search direction (TSD) method, of standard use in many electronic structure approaches with localization constraints, relies on the approximation that the truncated search direction vectors of the unconstrained problem resemble the exact search direction vectors of the constrained problem. With the TSD method, in order to maintain the localization constraints, a part of the precalculated information that is stored in the search direction vectors has to be deleted via an ad hoc, nonvariational truncation step. The results on an extensive set of test molecules show that, in general, calculations with the VLSD method require less iterations to converge than with the TSD method for any size of the localization region. It was found that in calculations on certain systems where the TSD method is forced to delete a very large amount of information, the VLSD method is capable of achieving convergence in up to three times less iterations. Validation tests show that structural and electronic properties calculated with either method are accurate and in agreement with other electronic structure approaches.

Timedependent resonant scattering: An analytical approach
View Description Hide DescriptionA timedependent description is given of a scattering process involving a single resonance embedded in a set of flat continua. An analytical approach is presented which starts from an incident free particle wave packet and yields the BreitWigner crosssection formula at infinite times. We show that at intermediate times the socalled WignerWeisskopf approximation is equivalent to a scattering process involving a contact potential. Applications in coldatom scattering and resonance enhanced desorption of molecules are discussed.

Chemical oscillator as a generalized Rayleigh oscillator
View Description Hide DescriptionWe derive the conditions under which a set of arbitrary two dimensional autonomous kinetic equations can be reduced to the form of a generalized Rayleigh oscillator which admits of limit cycle solution. This is based on a linear transformation of field variables which can be found by inspection of the kinetic equations. We illustrate the scheme with the help of several chemical and biochemical oscillator models to show how they can be cast as a generalized Rayleigh oscillator.

Coherentcontrol of linear signals: Frequencydomain analysis
View Description Hide DescriptionThe dependence of various types of linear signals on the phase profile of broadband optical pulses is examined using fundamental time translation invariance symmetry of multipoint correlation functions. The frequencydomain wavemixing analysis presented here unifies several arguments made earlier with respect to the conditions whereby coherent control schemes may be used.

Ionization potentials of semiconductors from firstprinciples
View Description Hide DescriptionThe ionization potential is the key to determine the absolute positions of valence and conduction bands of a semiconductor with respect to the vacuum level, which play a crucial role in physical and chemical properties of surfaces and interfaces. In spite of its farreaching significance, theoretical determination of ionization potentials has not attained as much attention as that of band gaps. In this work, a set of prototypical semiconductors are considered to establish the performance of the stateoftheart firstprinciples approaches. We have shown that in general KohnSham density functional theory with local density approximation or generalized gradient approximation (LDA/GGA) significantly underestimates the ionization potentials of semiconductors. When the quasiparticle correction from manybody perturbation theory in the GW approximation is taken into account, the agreement between theory and experiment can be greatly improved. We have made a critical comparison between two GW correction schemes, one taking into account the GW correction to the valence band maximum (VBM) of the bulk system, and the other based on the assumption that the LDA/GGA gives correct band gap center (BGC). Our study shows that the VBM scheme is better founded theoretically and leads to closer agreement with experiment practically than the BGC scheme. For semiconductors with shallow semicore states, for which the band gaps from the GW approach also exhibit significant errors, there is still significant discrepancy between GW and experiment, indicating the necessity to go beyond the standard GW approach for these materials.

Onthefly ab intito calculations of anharmonic vibrational frequencies: Localmonomer theory and application to HCl clusters
View Description Hide DescriptionWe present an onthefly quantum mechanical method to obtain anharmonic vibrational frequencies for molecular clusters. The basis for the method is the localmonomer model, a “divide and conquer” approach to theoretical spectroscopy, previously applied using fulldimensional surfaces [Y. Wang and J. M. Bowman, J. Chem. Phys.134, 154510 (2011)]. The model consists of performing a local normalmode analysis for each monomer in a cluster in the field of the surrounding monomers. Anharmonic vibrational frequencies are then determined for each monomer by numerically solving the Schrödinger equation in terms of the local coordinates using ab initio energies obtained directly. Residual monomermonomer coupling is accounted for using the Hückelcoupling extension [Y. Wang and J. M. Bowman, J. Chem. Phys.136, 144113 (2012)]. In addition to the direct localmonomer approach, we propose and demonstrate a composite ab initio technique to reduce computational costs for calculating the anharmonic frequencies of large clusters. This technique utilizes two ab initio methods, a lower level of theory to compute geometries and perform harmonic analyses and a subsequent higher level of theory to compute the energies used in the anharmonic frequency calculations. We demonstrate the onthefly approach on hydrogen chloride clusters ranging in size from the dimer to the hexamer. Comparisons of the theoretical frequencies are made to previous experiments. We find the method to be an effective and computationally efficient approach to compute anharmonic frequencies.

Efficient and accurate treatment of weak pairs in local CCSD(T) calculations
View Description Hide DescriptionLocal coupled cluster theory is based on (i) a restriction of the list of pairs (or triples) of occupied molecular orbitals, and (ii) a truncation of the virtual space to orbital pair (or triple) specific subspaces. The latter is motivated by an exponential decay of the contributions to the pair energy with respect to the distance between related local occupied and virtual orbitals; the former only by a polynomial R ^{−6} decay with respect to the distance R between the two occupied orbitals of the pair. Consequently, the restriction of the pair list is more critical, and contributions of pairs should not be neglected unless the corresponding interorbital distance is really large. In local coupled cluster theory pairs are usually discriminated on the basis of the interorbital distance, or the size of the 2nd order MøllerPlesset perturbation theory (MP2) estimate of the pair energy. Only strong pairs are treated at the full coupled cluster level, while weak pairs are treated just at the level of MP2. Yet MP2 might be problematic in certain cases, for example, πstacking is badly described by MP2, etc. We propose to substitute the MP2 treatment of weak pairs by an approach based on ringCCD by including thirdorder diagrams with R ^{−6} decay behavior. Such an approach is clearly superior; it provides higher accuracy, while the computational cost is not significantly higher than that of a MP2 based treatment of weak pairs.

Apparent violation of the sum rule for exchangecorrelation charges by generalized gradient approximations
View Description Hide DescriptionThe exchangecorrelation potential of Kohn–Sham densityfunctional theory, v XC(r), can be thought of as an electrostatic potential produced by the static charge distribution q XC(r) = −(1/4π)∇^{2} v XC(r). The total exchangecorrelation charge, Q XC = ∫q XC(r) d r, determines the rate of the asymptotic decay of v XC(r). If Q XC ≠ 0, the potential falls off as Q XC/r; if Q XC = 0, the decay is faster than coulombic. According to this rule, exchangecorrelation potentials derived from standard generalized gradient approximations (GGAs) should have Q XC = 0, but accurate numerical calculations give Q XC ≠ 0. We resolve this paradox by showing that the charge density q XC(r) associated with every GGA consists of two types of contributions: a continuous distribution and point charges arising from the singularities of v XC(r) at each nucleus. Numerical integration of q XC(r) accounts for the continuous charge but misses the point charges. When the pointcharge contributions are included, one obtains the correct Q XC value. These findings provide an important caveat for attempts to devise asymptotically correct Kohn–Sham potentials by modeling the distribution q XC(r).

Nonperturbative treatment of molecules in linear magnetic fields: Calculation of anapole susceptibilities
View Description Hide DescriptionIn the present study a nonperturbative approach to ab initio calculations of molecules in strong, linearly varying, magnetic fields is developed. The use of London atomic orbitals (LAOs) for nonuniform magnetic fields is discussed and the standard rationale of gaugeorigin invariance is generalized to invariance under arbitrary constant shifts of the magnetic vector potential. Our approach is applied to study magnetically induced anapole moments (or toroidal moments) and the related anapole susceptibilities for a test set of chiral and nonchiral molecules. For the first time numerical anapole moments are accessible on an ab initio level of theory. Our results show that the use of London atomic orbitals dramatically improves the basis set convergence also for magnetic properties related to nonuniform magnetic fields, at the cost that the Hellmann–Feynman theorem does not apply for a finite LAO basis set. It is shown that the mixed anapole susceptibility can be related to chirality, since its trace vanishes for an achiral molecule.

An algorithm for nonBornOppenheimer quantum mechanical variational calculations of N = 1 rotationally excited states of diatomic molecules using allparticle explicitly correlated Gaussian functions
View Description Hide DescriptionAn algorithm for quantum mechanical variational calculations of bound states of diatomic molecules corresponding to the total angular momentum quantum number equal to one (N = 1) is derived and implemented. The approach employs allparticle explicitly correlated Gaussian function for the wavefunction expansion. The algorithm is tested in the calculations of the N = 1, v = 0, …, 22 states of the HD^{+} ion.

Single molecule counting statistics for systems with periodic driving
View Description Hide DescriptionWe extend the generating function approach for calculation of event statistics observed in single molecule spectroscopy to cases where the single molecule evolves under explicitly timedependent and periodic perturbation. Floquet theory is used to recast the generating function equations for the periodically driven system into effective equations devoid of explicit timedependence. Two examples are considered, one employing simple stochastic dynamics and the other quantum dynamics, to demonstrate the versatility and numerical accuracy of the methodology.