Showing papers in "Journal of Chemical Physics in 2011"

Accurate and efficient algorithm for Bader charge integration

Abstract: We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume) and as a weight for the discrete integration of functions over the Bader volume. Compared with other grid-based algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to nonuniform grids, such as from a mesh-refinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.

Atom-centered symmetry functions for constructing high-dimensional neural network potentials

Abstract: Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calculations, and thus enable molecular dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the atomic positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as molecules, crystalline and amorphous solids, and liquids.

Markov models of molecular kinetics: Generation and validation

Abstract: Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.

Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals

Abstract: A systematic study of techniques for treating noncovalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for molecular complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 [revised in J. Chem. Phys. 132, 144104 (2010)] and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein–ligand reaction site (HSG), comprise the chemical systems for this work. From evaluati...

An overlap fitted chain of spheres exchange method.

Abstract: The “chain of spheres” (COS) algorithm, as part of the RIJCOSX SCF procedure, approximates the exchange term by performing analytic integration with respect to the coordinates of only one of the two electrons, whereas for the remaining coordinates, integration is carried out numerically. In the present work, we attempt to enhance the efficiency of the method by minimizing numerical errors in the COS procedure. The main idea is based on the work of Friesner and consists of finding a fitting matrix, Q, which leads the numerical and analytically evaluated overlap matrices to coincide. Using Q, the evaluation of exchange integrals can indeed be improved. Improved results and timings are obtained with the present default grid setup for both single point calculations and geometry optimizations. The fitting procedure results in a reduction of grid sizes necessary for achieving chemical accuracy. We demonstrate this by testing a number of grids and comparing results to the fully analytic and the earlier COS approximations. This turns out to be favourable for total and reaction energies, for which chemical accuracy can now be reached with a corresponding ∼30% speedup over the original RIJCOSX procedure for single point energies. Results are slightly less favourable for the accuracy of geometry optimizations, but the procedure is still shown to yield geometries with errors well below the method inherent errors of the employed theoretical framework.

Extended multi-configuration quasi-degenerate perturbation theory: the new approach to multi-state multi-reference perturbation theory.

Abstract: The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 11A′ – 21A′ conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 11A1 to 21A1 electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.

Electrical conductivity in Li2O2 and its role in determining capacity limitations in non-aqueous Li-O2 batteries.

Abstract: Non-aqueous Li-air or Li-O(2) cells show considerable promise as a very high energy density battery couple. Such cells, however, show sudden death at capacities far below their theoretical capacity and this, among other problems, limits their practicality. In this paper, we show that this sudden death arises from limited charge transport through the growing Li(2)O(2) film to the Li(2)O(2)-electrolyte interface, and this limitation defines a critical film thickness, above which it is not possible to support electrochemistry at the Li(2)O(2)-electrolyte interface. We report both electrochemical experiments using a reversible internal redox couple and a first principles metal-insulator-metal charge transport model to probe the electrical conductivity through Li(2)O(2) films produced during Li-O(2) discharge. Both experiment and theory show a "sudden death" in charge transport when film thickness is ~5 to 10 nm. The theoretical model shows that this occurs when the tunneling current through the film can no longer support the electrochemical current. Thus, engineering charge transport through Li(2)O(2) is a serious challenge if Li-O(2) batteries are ever to reach their potential.

Structural, mechanical, and thermodynamic properties of a coarse-grained DNA model

Abstract: We explore in detail the structural, mechanical, and thermodynamic properties of a coarse-grained model of DNA similar to that recently introduced in a study of DNA nanotweezers [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 134, 178101 (2010)]. Effective interactions are used to represent chain connectivity, excluded volume, base stacking, and hydrogen bonding, naturally reproducing a range of DNA behavior. The model incorporates the specificity of Watson–Crick base pairing, but otherwise neglects sequence dependence of interaction strengths, resulting in an “average base” description of DNA. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization, and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the elastic torsional and stretching moduli of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bas...

Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients

Abstract: The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Abstract: Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Basis set convergence of the coupled-cluster correction, δMP2CCSD(T): Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases

Abstract: In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a “coupled-cluster correction,” δMP2CCSD(T), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δMP2CCSD(T) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δMP2−F12CCSD(T*)−F12 correction, yielding a mean absolute deviation of 0.11 kcal mol−1 for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δMP2CCSD(T) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δMP2CCSD(T) corrections before the turning point, general...

Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: I. Statics.

Abstract: Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, [linear span]R(g)(2)[linear span], was found to scale as N(4/5) for an intermediate regime and N(2/3) for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204905 (2011)]. Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer

Abstract: We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian.

Improved hybrid functional for solids: The HSEsol functional

Abstract: We introduce the hybrid functional HSEsol. It is based on PBEsol, a revised Perdew–Burke–Ernzerhof functional, designed to yield accurate equilibrium properties for solids and their surfaces. We present lattice constants, bulk moduli, atomization energies, heats of formation, and band gaps for extended systems, as well as atomization energies for the molecular G2-1 test set. Compared to HSE, significant improvements are found for lattice constants and atomization energies of solids, but atomization energies of molecules are slightly worse than for HSE. Additionally, we present zero-point anharmonic expansion corrections to the lattice constants and bulk moduli, evaluated from ab initio phonon calculations.

Multilayer multiconfiguration time-dependent Hartree method: implementation and applications to a Henon-Heiles hamiltonian and to pyrazine.

Abstract: The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. 128, 164116 (2008)] is presented. The method is applied first to a generalized Henon–Heiles (HH) Hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH Hamiltonian using a seven-layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D Hamiltonian of Raab et al. [J. Chem. Phys. 110, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with 4.6×107time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only 4.5×105 coefficients and requiring a shorter computation time.

Determination of reaction coordinates via locally scaled diffusion map

Abstract: We present a multiscale method for the determination of collective reaction coordinates for macromolecular dynamics based on two recently developed mathematical techniques: diffusion map and the determination of local intrinsic dimensionality of large datasets. Our method accounts for the local variation of molecular configuration space, and the resulting global coordinates are correlated with the time scales of the molecular motion. To illustrate the approach, we present results for two model systems: all-atom alanine dipeptide and coarse-grained src homology 3 protein domain. We provide clear physical interpretation for the emerging coordinates and use them to calculate transition rates. The technique is general enough to be applied to any system for which a Boltzmann-sampled set of molecular configurations is available.

A generalized-gradient approximation exchange hole model for dispersion coefficients.

Abstract: A simple method for computing accurate density-dependent dispersion coefficients is presented. The dispersion coefficients are modeled by a generalized gradient-type approximation to Becke and Johnson's exchange hole dipole moment formalism. Our most cost-effective variant, based on a disjoint description of atoms in a molecule, gives mean absolute errors in the C6 coefficients for 90 complexes below 10%. The inclusion of the missing long-range van der Waals interactions in density functionals using the derived coefficients in a pair wise correction leads to highly accurate typical noncovalent interaction energies.

Hybrid functional investigations of band gaps and band alignments for AlN, GaN, InN, and InGaN.

Abstract: 20) a-plane] is thoroughly investigated. We find that for the relaxed surfaces of the binary nitrides the difference in electron affinities between m- and a-plane is less than 0.1 eV. The absolute electron affinities are found to strongly depend on the choice of XC functional. However, we find that relative alignments are less sensitive to the choice of XC functional. In particular, we find that relative alignments may be calculated based on Perdew–Becke–Ernzerhof [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 134, 3865 (1996)] surface calculations with the HSE06 lattice parameters. For InGaN we find that the VBM is a linear function of In content and that the majority of the band-gap bowing is located in the CBM. Based on the calculated electron affinities we predict that InGaN will be suited for water splitting up to 50% In content. © 2011 American Institute of Physics. [doi:10.1063/1.3548872]

All-boron analogues of aromatic hydrocarbons: B17- and B18-.

Abstract: We have investigated the structural and electronic properties of the B17− and B18− clusters using photoelectron spectroscopy (PES) and ab initio calculations. The adiabatic electron detachment energies of B17− and B18− are measured to be 4.23 ± 0.02 and 3.53 ± 0.05 eV, respectively. Calculated electron detachment energies are compared with experimental data, confirming the presence of one planar C2v (1A1) isomer for B17− and two nearly isoenergetic quasi-planar C3v (2A1) and Cs (2A′) isomers for B18−. The stability and planarity/quasi-planarity of B17− and B18− are ascribed to σ- and π-aromaticity. Chemical bonding analyses reveal that the nature of π-bonding in B17− and B18− is similar to that in the recently elucidated B162− and B19− clusters, respectively. The planar B17− cluster can be considered as an all-boron analogue of naphthalene, whereas the π-bonding in the quasi-planar B18− is reminiscent of that in coronene.

Density, structure, and dynamics of water: The effect of van der Waals interactions

Abstract: It is known that ab initio molecular dynamics (AIMD) simulations of liquid water at ambient conditions, based on the generalized gradient approximation (GGA) to density functional theory (DFT), with commonly used functionals fail to produce structural and diffusive properties in reasonable agreement with experiment. This is true for canonical, constant temperature simulations where the density of the liquid is fixed to the experimental density. The equilibrium density, at ambient conditions, of DFT water has recently been shown by Schmidt et al. [J. Phys. Chem. B, 113, 11959 (2009)] to be underestimated by different GGA functionals for exchange and correlation, and corrected by the addition of interatomic pair potentials to describe van der Waals (vdW) interactions. In this contribution we present a DFT-AIMD study of liquid water using several GGA functionals as well as the van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. As expected, we find that the density of water is grossly underestimated by GGA functionals. When a vdW-DF is used, the density improves drastically and the experimental diffusivity is reproduced without the need of thermal corrections. We analyze the origin of the density differences between all the functionals. We show that the vdW-DF increases the population of non-H-bonded interstitial sites, at distances between the first and second coordination shells. However, it excessively weakens the H-bond network, collapsing the second coordination shell. This structural problem is partially associated to the choice of GGA exchange in the vdW-DF. We show that a different choice for the exchange functional is enough to achieve an overall improvement both in structure and diffusivity.

Perspective: Water cluster mediated atmospheric chemistry

Abstract: The importance of water in atmospheric and environmental chemistry initiated recent studies with results documenting catalysis, suppression and anti-catalysis of thermal and photochemical reactions due to hydrogen bonding of reagents with water. Water, even one water molecule in binary complexes, has been shown by quantum chemistry to stabilize the transition state and lower its energy. However, new results underscore the need to evaluate the relative competing rates between reaction and dissipation to elucidate the role of water in chemistry. Water clusters have been used successfully as models for reactions in gas-phase, in aqueous condensed phases and at aqueous surfaces. Opportunities for experimental and theoretical chemical physics to make fundamental new discoveries abound. Work in this field is timely given the importance of water in atmospheric and environmental chemistry.

Quantum mechanical embedding theory based on a unique embedding potential

Abstract: We remove the nonuniqueness of the embedding potential that exists in most previous quantum mechanical embedding schemes by letting the environment and embedded region share a common embedding (interaction) potential. To efficiently solve for the embedding potential, an optimized effective potential method is derived. This embedding potential, which eschews use of approximate kinetic energy density functionals, is then used to describe the environment while a correlated wavefunction (CW) treatment of the embedded region is employed. We first demonstrate the accuracy of this new embedded CW (ECW) method by calculating the van der Waals binding energy curve between a hydrogen molecule and a hydrogen chain. We then examine the prototypical adsorption of CO on a metal surface, here the Cu(111) surface. In addition to obtaining proper site ordering (top site most stable) and binding energies within this theory, the ECW exhibits dramatic changes in the p-character of the CO 4σ and 5σ orbitals upon adsorption that agree very well with x-ray emission spectra, providing further validation of the theory. Finally, we generalize our embedding theory to spin-polarized quantum systems and discuss the connection between our theory and partition density functional theory.

An efficient local coupled cluster method for accurate thermochemistry of large systems

Abstract: An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described All required two-electron integrals are evaluated using density fitting approximations These have a negligible effect on the accuracy but reduce the computational effort by 1–2 orders of magnitude, as compared to standard integral-direct methods Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation) Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment The remaining close and weak pairs are approximated by LMP2 (local second-order Moller-Plesset perturbation theory); very distant pairs are neglected It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size If local density fitting approximations are activated, this is reduced to linear scaling The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented

On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies

Abstract: The leading cause of error in standard coupled cluster theory calculations of thermodynamic properties such as atomization energies and heats of formation originates with the truncation of the one-particle basis set expansion. Unfortunately, the use of finite basis sets is currently a computational necessity. Even with basis sets of quadruple zeta quality, errors can easily exceed 8 kcal/mol in small molecules, rendering the results of little practical use. Attempts to address this serious problem have led to a wide variety of proposals for simple complete basis set extrapolation formulas that exploit the regularity in the correlation consistent sequence of basis sets. This study explores the effectiveness of six formulas for reproducing the complete basis set limit. The W4 approach was also examined, although in lesser detail. Reference atomization energies were obtained from standard coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) calculations involving basis sets of 6ζ or better quality for a collection of 141 molecules. In addition, a subset of 51 atomization energies was treated with explicitly correlated CCSD(T)-F12b calculations and very large basis sets. Of the formulas considered, all proved reliable at reducing the one-particle expansion error. Even the least effective formulas cut the error in the raw values by more than half, a feat requiring a much larger basis set without the aid of extrapolation. The most effective formulas cut the mean absolute deviation by a further factor of two. Careful examination of the complete body of statistics failed to reveal a single choice that out performed the others for all basis set combinations and all classes of molecules.

Long-range corrected hybrid functionals for π-conjugated systems: dependence of the range-separation parameter on conjugation length.

Abstract: Long-range corrected (range-separated hybrid) functionals represent a relatively new class of functionals for generalized Kohn-Sham theory that have proven to be very successful, for instance, when it comes to predicting ionization potentials and energy gaps for a wide range of molecules and solids. The results obtained from long-range corrected density functional theory approaches can be improved dramatically, if the range-separation parameter (ω) is optimized for each system separately. In this work, we have optimized ω for a series of π-conjugated molecular systems of increasing length by forcing the resulting functionals to obey the ionization potential-theorem, i.e., that their highest occupied eigenvalue be equal to the ΔSCF ionization potential. The optimized ω values are observed to vary substantially from their default values for the functionals. For highly conjugated chains such as oligoacenes and polyenes, we find that the characteristic length scale of the range-separation, i.e., 1/ω, grows almost linearly with the number of repeat units, for saturated alkane chains, however, 1/ω quickly saturates after 5-6 repeat units. For oligothiophenes, we find that 1/ω grows linearly for the shorter oligomers but then saturates at around 10 repeat units. Our results point to a close relation between the optimal range-separation parameter and the degree of conjugation in the system.

Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer

Abstract: We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.

Communication: A global hybrid generalized gradient approximation to the exchange-correlation functional that satisfies the second-order density-gradient constraint and has broad applicability in chemistry

Abstract: We extend our recent SOGGA11 approximation to the exchange-correlation functional to include a percentage of Hartree-Fock exchange. The new functional, called SOGGA11-X, has better overall performance for a broad chemical database than any previously available global hybrid generalized gradient approximation, and in addition it satisfies an extra physical constraint in that it is correct to second order in the density-gradient.

The nature of singlet excitons in oligoacene molecular crystals.

Abstract: A theory for polarized absorption in crystalline oligoacenes is presented, which includes Frenkel exciton coupling, the coupling between Frenkel and charge-transfer (CT) excitons, and the coupling of all neutral and ionic excited states to the dominant ring-breathing vibrational mode. For tetracene, spectra calculated using all Frenkel couplings among the five lowest energy molecular singlet states predict a Davydov splitting (DS) of the lowest energy (0–0) vibronic band of only −32 cm−1, far smaller than the measured value of 631 cm−1 and of the wrong sign—a negative sign indicating that the polarizations of the lower and upper Davydov components are reversed from experiment. Inclusion of Frenkel-CT coupling dramatically improves the agreement with experiment, yielding a 0–0 DS of 601 cm−1 and a nearly quantitative reproduction of the relative spectral intensities of the 0–n vibronic components. Our analysis also shows that CT mixing increases with the size of the oligoacenes. We discuss the implications...

Markov State Models Based on Milestoning

Abstract: Markov state models (MSMs) have become the tool of choice to analyze large amounts of molecular dynamics data by approximating them as a Markov jump process between suitably predefined states. Here we investigate “Core Set MSMs,” a new type of MSMs that build on metastable core sets acting as milestones for tracing the rare event kinetics. We present a thorough analysis of Core Set MSMs based on the existing milestoning framework, Bayesian estimation methods and Transition Path Theory (TPT). We show that Core Set MSMs can be used to extract phenomenological rate constants between the metastable sets of the system and to approximate the evolution of certain key observables. The performance of Core Set MSMs in comparison to standard MSMs is analyzed and illustrated on a toy example and in the context of the torsion angle dynamics of alanine dipeptide.

A new approach to decoherence and momentum rescaling in the surface hopping algorithm.

Abstract: As originally proposed, the fewest switches surface hopping (FSSH) algorithm does not allow for decoherence between wavefunction amplitudes on different adiabatic surfaces. In this paper, we propose an inexpensive correction to standard FSSH dynamics wherein we explicitly model the decoherence of nuclear wave packets on distinct electronic surfaces. Our augmented fewest switches surface hopping approach is conceptually simple and, thus far, it has allowed us to capture several key features of the exact quantum results. Two points in particular merit attention. First, we obtain the correct branching ratios when a quantum particle passes through more than one region of nonadiabatic coupling. Second, our formalism provides a new and natural approach for rescaling nuclear momenta after a surface hop. Both of these features should become increasingly important as surface hopping schemes are applied to higher-dimensional problems.