Volume 138, Issue 13, 07 April 2013
 COMMUNICATIONS


Communication: A full solution of the annihilation reaction A + B → ∅ based on timesubordination
View Description Hide DescriptionThe connection between the governing equations of chemical reaction and the underlying stochastic processes of particle collision and transformation have been developed previously along two endmember conditions: perfectly mixed and maximally diffusionlimited. The complete governing equation recognizes that in the perfectly mixed case, the particle (i.e., molecular or macroparticle) number state evolution is Markovian, but that spatial selforganization of reactants decreases the probability of reactant pairs finding themselves colocated. This decreased probability manifests itself as a subordination of the clock time: as reactant concentrations become spatially variable (unmixed), the time required for reactants to find each other increases and the random operational time that particles spend in the active reaction process is less than the clock time. For example, in the system A + B → ∅, a simple approximate calculation for the return time of a Brownian motion to a moving boundary allows a calculation of the operational time density, and the total solution is a subordination integral of the perfectlymixed solution with a modified inverse Gaussian subordinator. The system transitions from the wellmixed solution to the asymptotic diffusionlimited solution that decays as t ^{−d/4} in ddimensions.
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 ARTICLES

 Theoretical Methods and Algorithms

Modified Z method to calculate melting curve by molecular dynamics
View Description Hide DescriptionWe extend the recently proposed Z method of estimating the melting temperature from a complete liquid and propose a modified Z method to calculate the melting temperature from a solidliquid coexistence state. With the simulation box of rectangular parallelepiped, an initial structure of perfect lattice can run in the microcanonical ensemble to achieve steady solidliquid coexistence state. The melting pressure and temperature are estimated from the coexistence state. For the small system with 1280 atoms, the simulation results show that the melting curve of copper has a good agreement with the experiments and is identical in accuracy with the results of the twophase coexistence method with 24 000 atoms in the literature. Moreover, the method is conceptually simpler than the twophase coexistence method.

Capturing static and dynamic correlations by a combination of projected HartreeFock and density functional theories
View Description Hide DescriptionThis paper explores the possibility of combining projected HartreeFock and density functional theories for treating static and dynamic correlations in molecular systems with meanfield computational cost. The combination of spinprojected unrestricted HartreeFock (SUHF) with the TPSS correlation functional (SUHF+TPSS) yields excellent results for nonmetallic molecular dissociations and singlettriplet splittings. However, SUHF+TPSS fails to provide the qualitatively correct dissociation curve for the notoriously difficult case of the chromium dimer. By tuning the TPSS correlation parameters and adding complex conjugation symmetry breaking and restoration to SUHF, the right curve shape for Cr_{2} can be obtained; unfortunately, such a combination is found to lead to overcorrelation in the general case.

Outofequilibrium catalysis of chemical reactions by electronic tunnel currents
View Description Hide DescriptionWe present an escape rate theory for currentinduced chemical reactions. We use Keldysh nonequilibrium Green's functions to derive a Langevin equation for the reaction coordinate. Due to the out of equilibrium electronic degrees of freedom, the friction, noise, and effective temperature in the Langevin equation depend locally on the reaction coordinate. As an example, we consider the dissociation of diatomic molecules induced by the electronic current from a scanning tunnelling microscope tip. In the resonant tunnelling regime, the molecular dissociation involves two processes which are intricately interconnected: a modification of the potential energy barrier and heating of the molecule. The decrease of the molecular barrier (i.e., the current induced catalytic reduction of the barrier) accompanied by the appearance of the effective, reactioncoordinatedependent temperature is an alternative mechanism for currentinduced chemical reactions, which is distinctly different from the usual paradigm of pumping vibrational degrees of freedom.

Bodyfixed relativistic molecular Hamiltonian and its application to nuclear spinrotation tensor
View Description Hide DescriptionA relativistic molecular Hamiltonian that describes electrons fully relativistically and nuclei quasirelativistically is proposed and transformed from the laboratory to the bodyfixed frame of reference. As a first application of the resulting bodyfixed relativistic molecular Hamiltonian, the long anticipated relativistic theory of nuclear spinrotation (NSR) tensor is formulated rigorously. A “relativistic mapping” between experimental NSR and NMR is further proposed, which is of great value in establishing highprecision absolute NMR shielding scales.

A climbing string method for saddle point search
View Description Hide DescriptionThe string method originally proposed for the computation of minimum energy paths (MEPs) is modified to find saddle points around a given minimum on a potential energy landscape using the location of this minimum as only input. In the modified method the string is evolved by gradient flow in path space, with one of its end points fixed at the minimum and the other end point (the climbing image) evolving towards a saddle point according to a modified potential force in which the component of the potential force in the tangent direction of the string is reversed. The use of a string allows us to monitor the evolution of the climbing image and prevent its escape from the basin of attraction of the minimum. This guarantees that the string always converges towards a MEP connecting the minimum to a saddle point lying on the boundary of the basin of attraction of this minimum. The convergence of the climbing image to the saddle point can also be accelerated by an inexact Newton method in the late stage of the computation. The performance of the numerical method is illustrated using the example of a 7atom cluster on a substrate. Comparison is made with the dimer method.

Microscopic derivation of particlebased coarsegrained dynamics
View Description Hide DescriptionIn this paper we revisit the derivation of equations of motion for coarsegrained (CG) particles from the microscopic Hamiltonian dynamics of the underlying atomistic system in equilibrium. The derivation is based on the projection operator method and timeconvolution equation. We demonstrate that due to the energy exchange between CG and intraparticle phase space coordinates in the microscopic system, the choice of projection operator is not unique, leading to different CG equations of motion that have the form of the nonlinear generalized Langevin equation (GLE). We derive the idempotence properties for the projection operators along the system trajectories and show that these properties result in streaming terms of the respective GLEs that are conservative forces and allow the expression of the nonconservative forces explicitly through thermodynamic averages, which can be measured from the microscopic simulations. The difference between GLEs that are presented herein lies in how the nonconservative forces are partitioned into dissipative and projected contributions. We compute the projected force and analyze conditions under which the projected (stochastic) force is orthogonal to (uncorrelated with) the momenta of CG particles, therefore justifying a transition to a framework of stochastic differential equations. We show that a position and momentumindependent memory function appears only if the projected force is fully decoupled from the past CG positions and momenta, respectively. In the case of nonvanishing correlations between the projected force and the CG coordinates in past times, we derive explicitly the position and momentumdependent memory function in a form of projection onto a space spanned by Norder Hermite polynomials. The expressions presented herein can be used to construct a hierarchy of thermodynamically consistent CG models with momentumdependent memory functions. They can also be used to design computational schemes for obtaining the parameters for GLEs and their variants such as dissipative particle dynamics equations from the microscopic data. We illustrate these applications by presenting the GLE with a memory function that is quadratic in the particle momenta.

Theoretical study of the nuclear spinmolecular rotation coupling for relativistic electrons and nonrelativistic nuclei. II. Quantitative results in HX (X=H,F,Cl,Br,I) compounds
View Description Hide DescriptionIn the present work, numerical results of the nuclear spinrotation (SR) tensor in the series of compounds HX (X=H,F,Cl,Br,I) within relativistic 4component expressions obtained by Aucar et al. [J. Chem. Phys.136, 204119 (Year: 2012)10.1063/1.4721627] are presented. The SR tensors of both the H and X nuclei are discussed. Calculations were carried out within the relativistic Linear Response formalism at the Random Phase Approximation with the DIRAC program. For the halogen nucleus X, correlation effects on the nonrelativistic values are shown to be of similar magnitude and opposite sign to relativistic effects. For the light H nucleus, by means of the linear response within the elimination of the small component approach it is shown that the whole relativistic effect is given by the spinorbit operator combined with the Fermi contact operator. Comparison of “best estimate” calculated values with experimental results yield differences smaller than 2%–3% in all cases. The validity of “Flygare's relation” linking the SR tensor and the NMR nuclear magnetic shielding tensor in the present series of compounds is analyzed.

Additional global internal contraction in variations of multireference equation of motion coupled cluster theory
View Description Hide DescriptionExtensions of multireference equation of motion coupled cluster theory (MREOMCC) [D. Datta and M. Nooijen, J. Chem. Phys.137, 204107 (Year: 2012)]10.1063/1.4766361 are presented that include additional correlation effects into the global, internally contracted similarity transformation, induced by the cluster operators. As a result the final uncontracted diagonalization space can be more compact than in the parent MREOMCC approach. A wide range of applications, including transition metal atomic excitation spectra, a large set of valence excited states of organic compounds, and potential energy surfaces of ground and excited states of butadiene, is presented to benchmark the applicability of the parent MREOMCC methodology and its new variations.

Direct simulation of protoncoupled electron transfer across multiple regimes
View Description Hide DescriptionThe coupled transfer of electrons and protons is a central feature of biological and molecular catalysis, yet fundamental aspects of these reactions remain poorly understood. In this study, we extend the ring polymer molecular dynamics (RPMD) method to enable direct simulation of protoncoupled electron transfer (PCET) reactions across a wide range of physically relevant regimes. In a systembath model for symmetric, colinear PCET in the condensed phase, RPMD trajectories reveal distinct kinetic pathways associated with sequential and concerted PCET reaction mechanisms, and it is demonstrated that concerted PCET proceeds by a solventgating mechanism in which the reorganization energy is mitigated by charge cancellation among the transferring particles. We further employ RPMD to study the kinetics and mechanistic features of concerted PCET reactions across multiple coupling regimes, including the fully nonadiabatic (both electronically and vibrationally nonadiabatic), partially adiabatic (electronically adiabatic, but vibrationally nonadiabatic), and fully adiabatic (both electronically and vibrationally adiabatic) limits. Comparison of RPMD with the results of PCET rate theories demonstrates the applicability of the direct simulation method over a broad range of conditions; it is particularly notable that RPMD accurately predicts the crossover in the thermal reaction rates between different coupling regimes while avoiding a priori assumptions about the PCET reaction mechanism. Finally, by utilizing the connections between RPMD rate theory and semiclassical instanton theory, we show that analysis of ringpolymer configurations in the RPMD transition path ensemble enables the a posteriori determination of the coupling regime for the PCET reaction. This analysis reveals an intriguing and distinct “transientprotonbridge” mechanism for concerted PCET that emerges in the transition between the protonmediated electron superexchange mechanism for fully nonadiabatic PCET and the hydrogen atom transfer mechanism for partially adiabatic PCET. Taken together, these results provide a unifying picture of the mechanisms and physical driving forces that govern PCET across a wide range of physical regimes, and they raise the possibility for PCET mechanisms that have not been previously reported.

Analysis of the forwardbackward trajectory solution for the mixed quantumclassical Liouville equation
View Description Hide DescriptionMixed quantumclassical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forwardbackward trajectory solution of the mixed quantumclassical Liouville equation in the mapping basis [C.Y. Hsieh and R. Kapral, J. Chem. Phys.137, 22A507 (Year: 2012)]10.1063/1.4736841 is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a meanfield potential determined jointly by the forward and backward trajectories. An analysis of the properties of this solution, numerical tests of its validity and an investigation of its utility for the study of nonadiabtic quantum processes are given. In addition, we present an extension of this approximate solution that allows one to systematically improve the results. This extension, termed the jump forwardbackward trajectory solution, is analyzed and tested in detail and its various implementations are discussed.

Valence excitation energies of alkenes, carbonyl compounds, and azabenzenes by timedependent density functional theory: Linear response of the ground state compared to collinear and noncollinear spinflip TDDFT with the TammDancoff approximation
View Description Hide DescriptionTimedependent density functional theory (TDDFT) holds great promise for studying photochemistry because of its affordable cost for large systems and for repeated calculations as required for direct dynamics. The chief obstacle is uncertain accuracy. There have been many validation studies, but there are also many formulations, and there have been few studies where several formulations were applied systematically to the same problems. Another issue, when TDDFT is applied with only a single exchangecorrelation functional, is that errors in the functional may mask successes or failures of the formulation. Here, to try to sort out some of the issues, we apply eight formulations of adiabatic TDDFT to the first valence excitations of ten molecules with 18 density functionals of diverse types. The formulations examined are linear response from the ground state (LRTDDFT), linear response from the ground state with the TammDancoff approximation (TDDFTTDA), the original collinear spinflip approximation with the TammDancoff (TD) approximation (SF1TDDFTTDA), the original noncollinear spinflip approximation with the TDA approximation (SF1NCTDDFTTDA), combined selfconsistentfield (SCF) and collinear spinflip calculations in the original spinprojected form (SF2TDDFTTDA) or nonspinprojected (NSF2TDDFTTDA), and combined SCF and noncollinear spinflip calculations (SF2NCTDDFTTDA and NSF2NCTDDFTTDA). Comparing LRTDDFT to TDDFTTDA, we observed that the excitation energy is raised by the TDA; this brings the excitation energies underestimated by full linear response closer to experiment, but sometimes it makes the results worse. For ethylene and butadiene, the excitation energies are underestimated by LRTDDFT, and the error becomes smaller making the TDA. Neither SF1TDDFTTDA nor SF2TDDFTTDA provides a lower mean unsigned error than LRTDDFT or TDDFTTDA. The comparison between collinear and noncollinear kernels shows that the noncollinear kernel drastically reduces the spin contamination in the systems considered here, and it makes the results more accurate than collinear spinflip TDDFT for functionals with a low percentage of HartreeFock exchange and sometimes for functionals with a higher percentage of HartreeFock exchange, but it yields less accurate results than groundstate TDDFT.

Accurate treatment of twodimensional nonseparable hindered internal rotors
View Description Hide DescriptionThis work presents an accurate way for calculating partition functions of strongly coupled hindered rotors in two dimensions. The twodimensional torsional potential is generated from electronic structure calculations and fitted to Fourier series. The kinetic energy includes offdiagonal terms which are allowed to vary with the torsional angles, and these terms were also fitted to Fourier series. The resulting Hamiltonian leads to a coupled Schrödinger equation which was solved by the variational method. Therefore, the final twodimensional nonseparable (2DNS) partition function incorporates coupling terms in both the kinetic and the potential energy. The methodology has been tested for propane, methyl formate, and a hydrogen abstraction transition state from propanone by the OH radical. How to incorporate the 2DNS partition function in the total vibrationalrotational partition function is also discussed.

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
View Description Hide DescriptionWe investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a onedimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of halfrenormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and πconjugated dendrimers) as well as nontree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In nontree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

Preselective screening for matrix elements in linearscaling exact exchange calculations
View Description Hide DescriptionWe present a simple but accurate preselection method based on Schwarz integral estimates to determine the significant elements of the exact exchange matrix before its evaluation, thus providing an asymptotical linearscaling behavior for nonmetallic systems. Our screening procedure proves to be highly suitable for exchange matrix calculations on massively parallel computing architectures, such as graphical processing units, for which we present a first linearscaling exchange matrix evaluation algorithm.

Band gaps from the TranBlaha modified BeckeJohnson approach: A systematic investigation
View Description Hide DescriptionThe semilocal BeckeJohnson (BJ) exchangecorrelation potential and its modified form proposed by Tran and Blaha (TBmBJ) have attracted a lot of interest recently because of the surprisingly accurate band gaps they can deliver for many semiconductors and insulators. In this work, we have investigated the performance of the TBmBJ potential for the description of electronic band structures in a comprehensive set of semiconductors and insulators. We point out that a perturbative use of the TBmBJ potential can give overall better results. By investigating a set of IIBVI and IIIV semiconductors, we point out that although the TBmBJ approach can describe the band gap of these materials quite well, the binding energies of semicore dstates in these materials deviate strongly from experiment. The difficulty of the TBmBJ potential to describe the localized states is likely the cause for the fact that the electronic band structures of Cu _{2}O and La_{2}O_{3} are still poorly described. Based on these observations, we propose to combine the TBmBJ approach with the Hubbard U correction for localized d/f states, which is able to provide overall good descriptions for both the band gaps and semicore states binding energies. We further apply the approach to calculate the band gaps of a set of Ti(IV)oxides, many of which have complicated structures so that the more advanced methods like GW are expensive to treat directly. An overall good agreement with experiment is obtained, which is remarkable considering its little computational efforts compared to GW.

Electrostatic frequency shifts in amide I vibrational spectra: Direct parameterization against experiment
View Description Hide DescriptionThe interpretation of protein amide I infrared spectra has been greatly assisted by the observation that the vibrational frequency of a peptide unit reports on its local electrostatic environment. However, the interpretation of spectra remains largely qualitative due to a lack of direct quantitative connections between computational models and experimental data. Here, we present an empirical parameterization of an electrostatic amide I frequency map derived from the infrared absorption spectra of 28 dipeptides. The observed frequency shifts are analyzed in terms of the local electrostatic potential, field, and field gradient, evaluated at sites near the amide bond in molecular dynamics simulations. We find that the frequency shifts observed in experiment correlate very well with the electric field in the direction of the C=O bond evaluated at the position of the amide oxygen atom. A linear bestfit mapping between observed frequencies and electric field yield sample standard deviations of 2.8 and 3.7 cm^{−1} for the CHARMM27 and OPLSAA force fields, respectively, and maximum deviations (within our data set) of 9 cm^{−1}. These results are discussed in the broader context of amide I vibrational models and the effort to produce quantitative agreement between simulated and experimental absorption spectra.

Accurate combinedhyperbolicinversepowerrepresentation of ab initio potential energy surface for the hydroperoxyl radical and dynamics study of reaction
View Description Hide DescriptionThe CombinedHyperbolicInversePowerRepresentation method, which treats evenly both short and longrange interactions, is used to fit an extensive set of ab initio points for HO_{2} previously utilized [Xu et al. , J. Chem. Phys.122, 244305 (Year: 2005)10.1063/1.1944290] to develop a spline interpolant. The novel form is shown to perform accurately when compared with others, while quasiclassical trajectory calculations of the O + OH reaction clearly pinpoint the role of longrange forces at low temperatures.

Bond breaking in a Morse chain under tension: Fragmentation patterns, higher index saddles, and bond healing
View Description Hide DescriptionWe investigate the fragmentation dynamics of an atomic chain under tensile stress. We have classified the location, stability type (indices), and energy of all equilibria for the general nparticle chain, and have highlighted the importance of saddle points with index >1. We show that for an n = 2particle chain under tensile stress the index 2 saddle plays a central role in organizing the dynamics. We apply normal form theory to analyze phase space structure and dynamics in a neighborhood of the index 2 saddle. We define a phase dividing surface (DS) that enables us to classify trajectories passing through a neighborhood of the saddle point using the values of the integrals associated with the normal form. We also generalize our definition of the dividing surface and define an extended dividing surface (EDS), which is used to sample and classify all trajectories that pass through a phase space neighborhood of the index 2 saddle at total energies less than that of the saddle. Classical trajectory simulations are used to study fragmentation patterns for the n = 2 chain under tension. That is, we investigate the relative probability for breaking one bond versus concerted fission of several (two, in this case) bonds. Initial conditions for trajectories are obtained by sampling the EDS at constant energy. We sample trajectories at fixed energies both above and below the energy of the saddle. The fate of trajectories (single versus multiple bond breakage) is explored as a function of the location of the initial condition on the EDS, and a connection made to the work of Chesnavich on collisioninduced dissociation. A significant finding is that we can readily identify trajectories that exhibit bond healing. Such trajectories pass outside the nominal (index 1) transition state for single bond dissociation, but return to the potential well region, possibly several times, before ultimately dissociating.

Unrestricted absolutely localized molecular orbitals for energy decomposition analysis: Theory and applications to intermolecular interactions involving radicals
View Description Hide DescriptionRadicalclosed shell and radicalradical intermolecular interactions are less wellunderstood than those between closed shell species. With the objective of gaining additional insight, this work reports a generalization of the absolutely localized molecular orbital (ALMO) energy decomposition analysis (EDA) to open shell fragments, described by selfconsistent field methods, such as standard density functional theory. The ALMOEDA variationally partitions an intermolecular interaction energy into three separate contributions; frozen orbital interactions, polarization, and charge transfer. The first examples involve comparison of the interactions of alkanes and alkyl radicals (methyl radical, methane, tertiary butyl radical, and isobutane) with sodium, potassium, hydronium, and ammonium cations. A second series of examples involve benzene cation interacting with a series of nucleophiles in both ontop and sideon geometries. The ALMOEDA yields a variety of interesting insights into the relative roles of its component contributions as the interacting partners and their geometries are changed.