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Showing papers in "Journal of Chemical Physics in 2007"


Journal ArticleDOI
TL;DR: In this paper, the authors present a new molecular dynamics algorithm for sampling the canonical distribution, where the velocities of all the particles are rescaled by a properly chosen random factor.
Abstract: The authors present a new molecular dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains constant during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liquid phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.

11,327 citations


Journal ArticleDOI
TL;DR: A library of Gaussian basis sets that has been specifically optimized to perform accurate molecular calculations based on density functional theory and can be used in first principles molecular dynamics simulations and is well suited for linear scaling calculations.
Abstract: We present a library of Gaussian basis sets that has been specifically optimized to perform accurate molecular calculations based on density functional theory. It targets a wide range of chemical environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition number of the overlap matrix for a set of molecules with respect to the exponents and contraction coefficients of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles molecular dynamics simulations and is well suited for linear scaling calculations.

2,700 citations


Journal ArticleDOI
TL;DR: The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li-F), second- (Na-Cl), and third-row main group (K, Ca, and Ga-Kr) atoms is presented and a significant improvement is found for 79 nonhydrogen systems.
Abstract: The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li–F), second- (Na–Cl), and third-row main group (K, Ca, and Ga–Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five ways. First, an extrapolation procedure is used to obtain the Hartree-Fock limit for inclusion in the total energy calculation. Second, the d-polarization sets are increased to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the latter. Third, the QCISD(T) method is replaced by the CCSD(T) method for the highest level of correlation treatment. Fourth, optimized geometries and zero-point energies are obtained with the B3LYP density functional. Fifth, two new higher level corrections are added to account for deficiencies in the energy calculations. The new method is ...

1,733 citations


Journal ArticleDOI
TL;DR: A new explicitly correlated CCSD(T)-F12 approximation is presented and tested for 23 molecules and 15 chemical reactions and the F12 correction strongly improves the basis set convergence of correlation and reaction energies.
Abstract: A new explicitly correlated CCSD(T)-F12 approximation is presented and tested for 23 molecules and 15 chemical reactions. The F12 correction strongly improves the basis set convergence of correlation and reaction energies. Errors of the Hartree-Fock contributions are effectively removed by including MP2 single excitations into the auxiliary basis set. Using aug-cc-pVTZ basis sets the CCSD(T)-F12 calculations are more accurate and two orders of magnitude faster than standard CCSD(T)/aug-cc-pV5Z calculations.

1,544 citations


Journal ArticleDOI
TL;DR: Scalar-relativistic pseudopotentials and corresponding spin-orbit potentials of the energy-consistent variety have been adjusted for the simulation of the 4d transition metal elements Y-Pd so as to reproduce atomic valence spectra from four-component all-electron calculations.
Abstract: Scalar-relativistic pseudopotentials and corresponding spin-orbit potentials of the energy-consistent variety have been adjusted for the simulation of the [Ar]3d(10) cores of the 4d transition metal elements Y-Pd. These potentials have been determined in a one-step procedure using numerical two-component calculations so as to reproduce atomic valence spectra from four-component all-electron calculations. The latter have been performed at the multi-configuration Dirac-Hartree-Fock level, using the Dirac-Coulomb Hamiltonian and perturbatively including the Breit interaction. The derived pseudopotentials reproduce the all-electron reference data with an average accuracy of 0.03 eV for configurational averages over nonrelativistic orbital configurations and 0.1 eV for individual relativistic states. Basis sets following a correlation consistent prescription have also been developed to accompany the new pseudopotentials. These range in size from cc-pVDZ-PP to cc-pV5Z-PP and also include sets for 4s4p correlation (cc-pwCVDZ-PP through cc-pwCV5Z-PP), as well as those with extra diffuse functions (aug-cc-pVDZ-PP, etc.). In order to accurately assess the impact of the pseudopotential approximation, all-electron basis sets of triple-zeta quality have also been developed using the Douglas-Kroll-Hess Hamiltonian (cc-pVTZ-DK, cc-pwCVTZ-DK, and aug-cc-pVTZ-DK). Benchmark calculations of atomic ionization potentials and 4d(m-2)5s(2)-->4d(m-1)5s(1) electronic excitation energies are reported at the coupled cluster level of theory with extrapolations to the complete basis set limit.

778 citations


Journal ArticleDOI
TL;DR: The TIP4P/2005 model is able to accurately describe the surface tension of water over the whole range of temperatures from the triple point to the critical temperature, and the test area is an appropriate methodological choice for the calculation of thesurface tension.
Abstract: We consider the calculation of the surface tension from simulations of several models of water, such as the traditional TIP3P, SPC, SPC/E, and TIP4P models, and the new generation of TIP4P-like models including the TIP4P/Ew, TIP4P/Ice, and TIP4P/2005. We employ a thermodynamic route proposed by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] to determine the surface tension that involves the estimate of the change in free energy associated with a small change in the interfacial area at constant volume. The values of the surface tension computed from this test-area method are found to be fully consistent with those obtained from the standard mechanical route, which is based on the evaluation of the components of the pressure tensor. We find that most models do not reproduce quantitatively the experimental values of the surface tension of water. The best description of the surface tension is given by those models that provide a better description of the vapor-liquid coexistence curve. The values of the surface tension for the SPC/E and TIP4P/Ew models are found to be in reasonably good agreement with the experimental values. From the present investigation, we conclude that the TIP4P/2005 model is able to accurately describe the surface tension of water over the whole range of temperatures from the triple point to the critical temperature. We also conclude that the test area is an appropriate methodological choice for the calculation of the surface tension not only for simple fluids, but also for complex molecular polar fluids, as is the case of water.

673 citations


Journal ArticleDOI
TL;DR: In this article, the authors present an automatic algorithm for the discovery of kinetically metastable states that is general applicable to solvated macromolecules, given molecular dynamics trajectories initiated from a well-defined starting distribution.
Abstract: To meet the challenge of modeling the conformational dynamics of biological macromolecules over long time scales, much recent effort has been devoted to constructing stochastic kinetic models, often in the form of discrete-state Markov models, from short molecular dynamics simulations. To construct useful models that faithfully represent dynamics at the time scales of interest, it is necessary to decompose configuration space into a set of kinetically metastable states. Previous attempts to define these states have relied upon either prior knowledge of the slow degrees of freedom or on the application of conformational clustering techniques which assume that conformationally distinct clusters are also kinetically distinct. Here, we present a first version of an automatic algorithm for the discovery of kinetically metastable states that is generally applicable to solvated macromolecules. Given molecular dynamics trajectories initiated from a well-defined starting distribution, the algorithm discovers long lived, kinetically metastable states through successive iterations of partitioning and aggregating conformation space into kinetically related regions. The authors apply this method to three peptides in explicit solvent—terminally blocked alanine, the 21-residue helical Fs peptide, and the engineered 12-residue β-hairpin trpzip2—to assess its ability to generate physically meaningful states and faithful kinetic models.

649 citations


Journal ArticleDOI
TL;DR: A simplified and improved version of the string method, originally proposed by E et al. (2002) for identifying the minimum energy paths in barrier-crossing events, that is more stable and accurate and combined with the climbing image technique for the accurate calculation of saddle points.
Abstract: We present a simplified and improved version of the string method, originally proposed by E et al. [Phys. Rev. B 66, 052301 (2002)] for identifying the minimum energy paths in barrier-crossing events. In this new version, the step of projecting the potential force to the direction normal to the string is eliminated and the full potential force is used in the evolution of the string. This not only simplifies the numerical procedure, but also makes the method more stable and accurate. We discuss the algorithmic details of the improved string method, analyze its stability, accuracy and efficiency, and illustrate it via numerical examples. We also show how the string method can be combined with the climbing image technique for the accurate calculation of saddle points and we present another algorithm for the accurate calculation of the unstable directions at the saddle points.

638 citations


Journal ArticleDOI
TL;DR: The G4(MP2) method provides an accurate and economical method for thermochemical predictions that has an overall accuracy for the G3/05 test set that is much better than G3( MP2) theory and even better thanG3 theory.
Abstract: Two modifications of Gaussian-4 (G4) theory [L. A. Curtiss et al., J. Chem. Phys. 126, 084108 (2007)] are presented in which second- and third-order perturbation theories are used in place of fourth-order perturbation theory. These two new methods are referred to as G4(MP2) and G4(MP3), respectively. Both methods have been assessed on the G3/05 test set of accurate experimental data. The average absolute deviation from experiment for the 454 energies in this test set is 1.04 kcalmol for G4(MP2) theory and 1.03 kcalmol for G4(MP3) theory compared to 0.83 kcalmol for G4 theory. G4(MP2) is slightly more accurate for enthalpies of formation than G4(MP3) (0.99 versus 1.04 kcalmol), while G4(MP3) is more accurate for ionization potentials and electron affinities. Overall, the G4(MP2) method provides an accurate and economical method for thermochemical predictions. It has an overall accuracy for the G3/05 test set that is much better than G3(MP2) theory (1.04 versus 1.39 kcalmol) and even better than G3 theory (1.04 versus 1.13 kcalmol). In addition, G4(MP2) does better for challenging hypervalent systems such as H(2)SO(4) and for nonhydrogen species than G3(MP2) theory.

594 citations


Journal ArticleDOI
TL;DR: A systematic procedure based on two-dimensional potentials of mean force for defining cutoffs for a given pair of distance and angular coordinates is developed and an electronic structure-based definition of hydrogen bonding in liquid water is developed, related to the electronic occupancy of the antibonding OH orbitals.
Abstract: X-ray and neutron diffractions, vibrational spectroscopy, and x-ray Raman scattering and absorption experiments on water are often interpreted in terms of hydrogen bonding. To this end a number of geometric definitions of hydrogen bonding in water have been developed. While all definitions of hydrogen bonding are to some extent arbitrary, those involving one distance and one angle for a given water dimer are unnecessarily so. In this paper the authors develop a systematic procedure based on two-dimensional potentials of mean force for defining cutoffs for a given pair of distance and angular coordinates. They also develop an electronic structure-based definition of hydrogen bonding in liquid water, related to the electronic occupancy of the antibonding OH orbitals. This definition turns out to be reasonably compatible with one of the distance-angle geometric definitions. These two definitions lead to an estimate of the number of hydrogen bonds per molecule in liquid simple point charge/extended (SPC/E) water of between 3.2 and 3.4. They also used these and other hydrogen-bond definitions to examine the dynamics of local hydrogen-bond number fluctuations, finding an approximate long-time decay constant for SPC/E water of between 0.8 and 0.9 ps, which corresponds to the time scale for local structural relaxation.

586 citations


Journal ArticleDOI
TL;DR: This paper quantifies many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms and demonstrates the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer.
Abstract: In the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of many-electron self-interaction error (SIE). In this paper, we quantify many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer. Semilocal approximations have the largest many-electron SIE, which is only slightly reduced in typical global hybrids. In these approximations the energy versus fractional electron number curves upward, while in Hartree-Fock theory the energy curves downward. Perdew-Zunger self-interaction correction [Phys. Rev. B 23, 5048 (1981)] significantly reduces the many-electron SIE of semilocal functionals but impairs their accuracy for equilibrium properties. In contrast, a long-range corrected hybrid functional can be nearly many-electron SIE-free in many cases (for reasons we discuss) and at the same time performs remarkably well for many molecular properties.

Journal ArticleDOI
TL;DR: The computational approach to the Hirshfeld atom in a molecule is critically investigated, and several difficulties are highlighted, and it is shown that these difficulties are mitigated by an alternative, iterative version, of the HirShfeld partitioning procedure.
Abstract: The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges.

Journal ArticleDOI
TL;DR: A decoherence correction is applied to the state probabilities, in conjunction with Tully's algorithm, and the authors obtain satisfactory results in terms of internal consistency and of agreement with the outcomes of quantum wave packet calculations.
Abstract: In this paper the authors address the problem of internal consistency in trajectory surface hopping methods, i.e., the requirement that the fraction of trajectories running on each electronic state equals the probabilities computed by the electronic time-dependent Schrodinger equation, after averaging over all trajectories. They derive a formula for the hopping probability in Tully’s “fewest switches” spirit that would yield a rigorously consistent treatment. They show the relationship of Tully’s widely used surface hopping algorithm with the “exact” prescription that cannot be applied when running each trajectory independently. They also bring out the connection of the consistency problem with the coherent propagation of the electronic wave function and the artifacts caused by coherent Rabi-type oscillations of the state probabilities in weak coupling regimes. A real molecule (azobenzene) and two ad hoc models serve as examples to illustrate the above theoretical arguments. Following a proposal by Truhla...

Journal ArticleDOI
TL;DR: The theoretical lattice constants overestimate the experimental ones by approximately 1%, and hence behave similarly to the PBE gradient-corrected exchange-correlation functional, and theoretical values for heats of formation for both the B3LYP as well as the B 3PW91 functionals are presented.
Abstract: The B3LYP hybrid functional has shown to successfully predict a wide range of molecular properties. For periodic systems, however, the failure to attain the exact homogeneous electron gas limit as well as the semiempirical construction turns out to be a major drawback of the functional. We rigorously assess the B3LYP functional for solids through calculations of lattice parameters, bulk moduli, and thermochemical properties (atomization energies and reaction energies). The theoretical lattice constants overestimate the experimental ones by approximately 1%, and hence behave similarly to the PBE gradient-corrected exchange-correlation functional. B3LYP atomization energies of solids are drastically worse than those of nonempirical hybrid Hartree-Fock/density functionals (HF/DFT) such as PBE0 and HSE03. These large errors can be traced back to the lack of a proper description of "free-electron-like" systems with a significant itinerant character (metals and small gap semiconductors). Similar calculations using the popular semiempirical B3PW91 hybrid functional, which fulfills the uniform electron gas limit, show a clear improvement over B3LYP regarding atomization energies. Finally, theoretical values for heats of formation for both the B3LYP as well as the B3PW91 functionals are presented. These document a most likely fortuitously good agreement with experiment for the B3LYP hybrid functional.

Journal ArticleDOI
TL;DR: A general form of orbital invariant explicitly correlated second-order closed-shell Moller-Plesset perturbation theory (MP2-F12) is derived, and compact working equations are presented.
Abstract: A general form of orbital invariant explicitly correlated second-order closed-shell Moller-Plesset perturbation theory (MP2-F12) is derived, and compact working equations are presented. Many-electron integrals are avoided by resolution of the identity (RI) approximations using the complementary auxiliary basis set approach. A hierarchy of well defined levels of approximation is introduced, differing from the exact theory by the neglect of terms involving matrix elements over the Fock operator. The most accurate method is denoted as MP2-F12/3B. This assumes only that Fock matrix elements between occupied orbitals and orbitals outside the auxiliary basis set are negligible. For the chosen ansatz for the first-order wave function this is exact if the auxiliary basis is complete. In the next lower approximation it is assumed that the occupied orbital space is closed under action of the Fock operator [generalized Brillouin condition (GBC)]; this is equivalent to approximation 2B of Klopper and Samson [J. Chem....

Journal ArticleDOI
TL;DR: A new method for searching low free energy paths in complex molecular systems at finite temperature is presented that combines features of approaches such as metadynamics or umbrella sampling with those of path based methods and introduces two variables that are able to describe the position of a point in configuration space relative to a preassigned path.
Abstract: The authors present a new method for searching low free energy paths in complex molecular systems at finite temperature. They introduce two variables that are able to describe the position of a point in configurational space relative to a preassigned path. With the help of these two variables the authors combine features of approaches such as metadynamics or umbrella sampling with those of path based methods. This allows global searches in the space of paths to be performed and a new variational principle for the determination of low free energy paths to be established. Contrary to metadynamics or umbrella sampling the path can be described by an arbitrary large number of variables, still the energy profile along the path can be calculated. The authors exemplify the method numerically by studying the conformational changes of alanine dipeptide.

Journal ArticleDOI
TL;DR: A new method is presented for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky rotation of the normal modes, able to provide fully converged spectra with a quite modest computational time, both in vacuo and in condensed phase.
Abstract: The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky [Acta Physicochim. URSS 7, 551 (1937)] rotation of the normal modes. The method automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a quite modest computational time, both in vacuo and in condensed phase. Starting from the rigorous time-dependent expression they discuss indeed in which limits the spectrum of a molecule embedded in a solvent, described as a polarizable continuum, can be computed in a time-independent formalism, defining both nonequilibrium and equilibrium limits. In these cases the polarizable continuum model provides a suitable description of the solvent field. By computing the absorption spectra of anthracene in gas phase and of coumarin C153 in gas phase and cyclohexane, and the phosphorescence spectrum of the unsubstituted coumarin in ethanol they show that the method is fast and efficient.

Journal ArticleDOI
TL;DR: A much more satisfying derivation founded on second-order perturbation theory in the closure approximation and a semiclassical evaluation of the relevant interaction integrals is presented.
Abstract: We have recently introduced a model of the dispersion interaction based on the position-dependent dipole moment of the exchange hole [J. Chem. Phys. 122, 154104 (2005)]. The original derivation, involving simple dipole-induced-dipole electrostatics, was somewhat heuristic, however, and lacking in rigor. Here we present a much more satisfying derivation founded on second-order perturbation theory in the closure approximation and a semiclassical evaluation of the relevant interaction integrals. Expressions for C6, C8, and C10 dispersion coefficients are obtained in a remarkably straightforward manner. Their values agree very well with ab initio reference data on dispersion coefficients between the atoms H, He, Ne, Ar, Kr, and Xe. We also highlight the importance of the exchange-hole contribution to the dispersion coefficients, especially to C6.

Journal ArticleDOI
TL;DR: In this article, a detailed investigation of the acene series using high-level wave function theory is presented, and an ab initio density matrix renormalization group algorithm is used to carry out complete active space calculations on the acenes from napthalene to dodecacene correlating the full π-valence space.
Abstract: We present a detailed investigation of the acene series using high-level wave function theory. Our ab initio density matrix renormalization group algorithm has enabled us to carry out complete active space calculations on the acenes from napthalene to dodecacene correlating the full π-valence space. While we find that the ground state is a singlet for all chain lengths, examination of several measures of radical character, including the natural orbitals, effective number of unpaired electrons, and various correlation functions, suggests that the longer acene ground states are polyradical in nature.

Journal ArticleDOI
TL;DR: The authors investigate the chemical reactivity of these zigzag edge sites by examining their reaction energetics with common radicals from first principles, and the validity of this concept is verified by comparing the dissociation energies of edge-radical bonds with similar bonds in molecules.
Abstract: The zigzag edge of a graphene nanoribbon possesses a unique electronic state that is near the Fermi level and localized at the edge carbon atoms. The authors investigate the chemical reactivity of these zigzag edge sites by examining their reaction energetics with common radicals from first principles. A "partial radical" concept for the edge carbon atoms is introduced to characterize their chemical reactivity, and the validity of this concept is verified by comparing the dissociation energies of edge-radical bonds with similar bonds in molecules. In addition, the uniqueness of the zigzag-edged graphene nanoribbon is further demonstrated by comparing it with other forms of sp2 carbons, including a graphene sheet, nanotubes, and an armchair-edged graphene nanoribbon.

Journal ArticleDOI
TL;DR: The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra, and applies the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom.
Abstract: The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Journal ArticleDOI
TL;DR: A state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of emission energies has been developed and coded in the framework of the so called polarizable continuum model (PCM).
Abstract: A state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of emission energies has been developed and coded in the framework of the so called polarizable continuum model (PCM). The new model allows for a rigorous and effective treatment of dynamical solvent effects in the computation of fluorescence and phosphorescence spectra in solution, and it can be used for studying different relaxation time regimes. SS and conventional linear response (LR) models have been compared by computing the emission energies for different benchmark systems (formaldehyde in water and three coumarin derivatives in ethanol). Special attention is given to the influence of dynamical solvation effects on LR geometry optimizations in solution. The results on formaldehyde point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents and/or weak transitions. The computed emission energies for coumarin derivatives are very close to their experimental counterparts, pointing out the importance of a proper treatment of nonequilibrium solvent effects on both the excited and the ground state energies. The availability of SS-PCM/TD-DFT models for the study of absorption and emission processes allows for a consistent treatment of a number of different spectroscopic properties in solution.

Journal ArticleDOI
TL;DR: Cl clustering based on kinetics is examined, merging configurational microstates together so as to identify long-lived, i.e., dynamically metastable, states, and an approach is proposed to generate a hierarchical model of networks, each having a different number of metastable states.
Abstract: Molecular dynamics simulation generates large quantities of data that must be interpreted using physically meaningful analysis. A common approach is to describe the system dynamics in terms of transitions between coarse partitions of conformational space. In contrast to previous work that partitions the space according to geometric proximity, the authors examine here clustering based on kinetics, merging configurational microstates together so as to identify long-lived, i.e., dynamically metastable, states. As test systems microsecond molecular dynamics simulations of the polyalanines Ala(8) and Ala(12) are analyzed. Both systems clearly exhibit metastability, with some kinetically distinct metastable states being geometrically very similar. Using the backbone torsion rotamer pattern to define the microstates, a definition is obtained of metastable states whose lifetimes considerably exceed the memory associated with interstate dynamics, thus allowing the kinetics to be described by a Markov model. This model is shown to be valid by comparison of its predictions with the kinetics obtained directly from the molecular dynamics simulations. In contrast, clustering based on the hydrogen-bonding pattern fails to identify long-lived metastable states or a reliable Markov model. Finally, an approach is proposed to generate a hierarchical model of networks, each having a different number of metastable states. The model hierarchy yields a qualitative understanding of the multiple time and length scales in the dynamics of biomolecules.

Journal ArticleDOI
TL;DR: Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts and the (D) correction often works in the right direction.
Abstract: Double-hybrid density functionals are based on a mixing of standard generalized gradient approximations (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixture of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), respectively. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chemistry applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent density functional theory (TD-DFT) or the closely related Tamm-Dancoff approximation (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to configuration interaction with...

Journal ArticleDOI
TL;DR: A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data that is the inverse of the center line slope (CLS) of the 2D spectrum and is essentially unaffected by Fourier filtering methods (apodization).
Abstract: Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.

Journal Article
TL;DR: In this article, a method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky [Acta Physicochim. URSS 7, 551 (1937)] rotation of the normal modes, is presented.
Abstract: The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky [Acta Physicochim. URSS 7, 551 (1937)] rotation of the normal modes. The method automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a quite modest computational time, both in vacuo and in condensed phase. Starting from the rigorous time-dependent expression they discuss indeed in which limits the spectrum of a molecule embedded in a solvent, described as a polarizable continuum, can be computed in a time-independent formalism, defining both nonequilibrium and equilibrium limits. In these cases the polarizable continuum model provides a suitable description of the solvent field. By computing the absorption spectra of anthracene in gas phase and of coumarin C153 in gas phase and cyclohexane, and the phosphorescence spectrum of the unsubstituted coumarin in ethanol they show that the method is fast and efficient.

Journal ArticleDOI
TL;DR: The authors present scalar-relativistic energy-consistent Hartree-Fock pseudopotentials for the main-group elements that are suitable for quantum Monte Carlo (QMC) calculations and demonstrate their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties.
Abstract: The authors present scalar-relativistic energy-consistent Hartree-Fock pseudopotentials for the main-group elements. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. They demonstrate their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties. In particular, they compute the vibrational frequencies and binding energies of 26 first- and second-row diatomic molecules using post-Hartree-Fock methods, finding excellent agreement with the corresponding all-electron values. They also show their pseudopotentials give superior accuracy than other existing pseudopotentials constructed specifically for QMC. Finally, valence basis sets of different sizes (VnZ with n=D,T,Q,5 for first and second rows, and n=D,T for third to fifth rows) optimized for our pseudopotentials are also presented.

Journal ArticleDOI
TL;DR: In this article, the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions, using this representation, a modified next reaction method is derived, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems having delays.
Abstract: Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie algorithm or the next reaction method. In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified next reaction method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays.

Journal ArticleDOI
Frank Neese1
TL;DR: A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values.
Abstract: The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.

Journal ArticleDOI
TL;DR: Refined parameters of an atomistic interaction potential model for the room temperature ionic liquid 1-n-butyl,3-methylimidazolium hexafluorophosphate are presented and the calculated diffusion coefficients of ions and the surface tension of the liquid agree well with experiment.
Abstract: Refined parameters of an atomistic interaction potential model for the room temperature ionic liquid 1-n-butyl,3-methylimidazolium hexafluorophosphate are presented. Classical molecular dynamics simulations have been carried out to validate this fully flexible all-atom model. It predicts the density of the liquid at different temperatures between 300 and 500 K within 1.4% of the experimental value. Intermolecular radial distribution functions and the spatial distribution functions obtained from the new model are in close agreement with ab initio simulations. The calculated diffusion coefficients of ions and the surface tension of the liquid agree well with experiment.