Showing papers in "Journal of Chemical Physics in 2008"
TL;DR: The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybriddensity functionals.
Abstract: A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some “difficult problems,” such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid density functionals.
2,852 citations
TL;DR: If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images.
Abstract: A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).
1,409 citations
TL;DR: The multistate Bennett acceptance ratio estimator (MBAR) as mentioned in this paper is an estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment.
Abstract: We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.
1,265 citations
TL;DR: The study highlights the ambiguous nature of the term "charge transfer," providing insight into the observation that while many charge-transfer excitations are poorly described by GGA and hybrid functionals, others are accurately reproduced.
Abstract: Electronic excitation energies are determined using the CAM-B3LYP Coulomb-attenuated functional [T. Yanai et al. Chem. Phys. Lett. 393, 51 (2004)], together with a standard generalized gradient approximation (GGA) and hybrid functional. The degree of spatial overlap between the occupied and virtual orbitals involved in an excitation is measured using a quantity Lambda, and the extent to which excitation energy errors correlate with Lambda is quantified. For a set of 59 excitations of local, Rydberg, and intramolecular charge-transfer character in 18 theoretically challenging main-group molecules, CAM-B3LYP provides by far the best overall performance; no correlation is observed between excitation energy errors and Lambda, reflecting the good quality, balanced description of all three categories of excitation. By contrast, a clear correlation is observed for the GGA and, to a lesser extent, the hybrid functional, allowing a simple diagnostic test to be proposed for judging the reliability of a general excitation from these functionals--when Lambda falls below a prescribed threshold, excitations are likely to be in very significant error. The study highlights the ambiguous nature of the term "charge transfer," providing insight into the observation that while many charge-transfer excitations are poorly described by GGA and hybrid functionals, others are accurately reproduced.
1,230 citations
TL;DR: A theoretical framework for studying the role of quantum interference effects in energy transfer dynamics of molecular arrays interacting with a thermal bath within the Lindblad formalism is developed and an effective interplay between the free Hamiltonian evolution and the thermal fluctuations in the environment is demonstrated.
Abstract: Energy transfer within photosynthetic systems can display quantum effects such as delocalized excitonic transport. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the Fenna-Matthews-Olson (FMO) protein complex [Engel et al., Nature (London) 446, 782 (2007)]. However, the relevance of quantum dynamical processes to the exciton transfer efficiency is to a large extent unknown. Here, we develop a theoretical framework for studying the role of quantum interference effects in energy transfer dynamics of molecular arrays interacting with a thermal bath within the Lindblad formalism. To this end, we generalize continuous-time quantum walks to nonunitary and temperature-dependent dynamics in Liouville space derived from a microscopic Hamiltonian. Different physical effects of coherence and decoherence processes are explored via a universal measure for the energy transfer efficiency and its susceptibility. In particular, we demonstrate that for the FMO complex, an effective interplay between the free Hamiltonian evolution and the thermal fluctuations in the environment leads to a substantial increase in energy transfer efficiency from about 70% to 99%.
1,145 citations
TL;DR: The new basis sets have been optimized for use with explicitly correlated F12 methods and are shown to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row.
Abstract: Correlation consistent basis sets have been optimized for use with explicitly correlated F12 methods. The new sets, denoted cc-pVnZ-F12 (n=D,T,Q), are similar in size and construction to the standard aug-cc-pVnZ and aug-cc-pV(n+d)Z basis sets, but the new sets are shown in the present work to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row. For molecules containing only first row atoms, the smallest cc-pVDZ-F12 basis set consistently recovers nearly 99% of the MP2 valence correlation energy when combined with the MP2-F12/3C method. The convergence with basis set for molecules containing second row atoms is slower, but the new DZ basis set still recovers 97%-99% of the frozen core MP2 correlation energy. The accuracy of the new basis sets for relative energetics is demonstrated in benchmark calculations on a set of 15 chemical reactions.
1,091 citations
TL;DR: In this article, a set of 28 medium-sized organic molecules is assembled that cover the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases.
Abstract: A benchmark set of 28 medium-sized organic molecules is assembled that covers the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. Vertical excitation energies and one-electron properties are computed for the valence excited states of these molecules using both multiconfigurational second-order perturbation theory, CASPT2, and a hierarchy of coupled cluster methods, CC2, CCSD, and CC3. The calculations are done at identical geometries (MP26-31G*) and with the same basis set (TZVP). In most cases, the CC3 results are very close to the CASPT2 results, whereas there are larger deviations with CC2 and CCSD, especially in singlet excited states that are not dominated by single excitations. Statistical evaluations of the calculated vertical excitation energies for 223 states are presented and discussed in order to assess the relative merits of the applied methods. CC2 reproduces the CC3 reference data for the singlets better than CCSD. On the basis of the current computational results and an extensive survey of the literature, we propose best estimates for the energies of 104 singlet and 63 triplet excited states.
860 citations
TL;DR: This review focuses on recent developments in the field of DNP with a special emphasis on work done at high magnetic fields (> or =5 T), the regime where contemporary NMR experiments are performed.
Abstract: Dynamic nuclear polarization (DNP) is a method that permits NMR signal intensities of solids and liquids to be enhanced significantly, and is therefore potentially an important tool in structural and mechanistic studies of biologically relevant molecules. During a DNP experiment, the large polarization of an exogeneous or endogeneous unpaired electron is transferred to the nuclei of interest (I) by microwave (microw) irradiation of the sample. The maximum theoretical enhancement achievable is given by the gyromagnetic ratios (gamma(e)gamma(l)), being approximately 660 for protons. In the early 1950s, the DNP phenomenon was demonstrated experimentally, and intensively investigated in the following four decades, primarily at low magnetic fields. This review focuses on recent developments in the field of DNP with a special emphasis on work done at high magnetic fields (> or =5 T), the regime where contemporary NMR experiments are performed. After a brief historical survey, we present a review of the classical continuous wave (cw) DNP mechanisms-the Overhauser effect, the solid effect, the cross effect, and thermal mixing. A special section is devoted to the theory of coherent polarization transfer mechanisms, since they are potentially more efficient at high fields than classical polarization schemes. The implementation of DNP at high magnetic fields has required the development and improvement of new and existing instrumentation. Therefore, we also review some recent developments in microw and probe technology, followed by an overview of DNP applications in biological solids and liquids. Finally, we outline some possible areas for future developments.
777 citations
TL;DR: In this paper, the complex bond order vectors are averaged over the first neighbor shell of a given particle and the particle itself, which improves the accuracy with which different crystal structures can be distinguished.
Abstract: Local bond order parameters based on spherical harmonics, also known as Steinhardt order parameters, are often used to determine crystal structures in molecular simulations. Here we propose a modification of this method in which the complex bond order vectors are averaged over the first neighbor shell of a given particle and the particle itself. As demonstrated using soft particle systems, this averaging procedure considerably improves the accuracy with which different crystal structures can be distinguished.
743 citations
TL;DR: The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for theMS-CG models.
Abstract: Coarse-grained (CG) models provide a computationally efficient method for rapidly investigating the long time- and length-scale processes that play a critical role in many important biological and soft matter processes Recently, Izvekov and Voth introduced a new multiscale coarse-graining (MS-CG) method [J Phys Chem B 109, 2469 (2005); J Chem Phys 123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MS-CG models A CG model that employs such a PMF as a “potential energy function” will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal These algorithms use computer simulation data from the atomically detailed model Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model
707 citations
TL;DR: The approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations.
Abstract: In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Phi and Psi in N-acetylalanyl-N'-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.
TL;DR: The relative entropy carries physical significance by using it to quantify the deviations of a three-site model of water from simple liquids, finding that the relative entropy, a thermodynamic concept, even predicts water's kinetic anomalies.
Abstract: We show that the relative entropy, S(rel) identical with Sigma(p(T)) ln(p(T)/p(M)), provides a fundamental and unifying framework for multiscale analysis and for inverse molecular-thermodynamic problems involving optimization of a model system (M) to reproduce the properties of a target one (T). We demonstrate that the relative entropy serves as a generating function for principles in variational mean-field theory and uniqueness and gives intuitive results for simple case scenarios in model development. Moreover, we suggest that the relative entropy provides a rigorous framework for multiscale simulations and offers new numerical techniques for linking models at different scales. Finally, we show that S(rel) carries physical significance by using it to quantify the deviations of a three-site model of water from simple liquids, finding that the relative entropy, a thermodynamic concept, even predicts water's kinetic anomalies.
TL;DR: The method presented here automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a modest computational requirement, performing for the first time an exact treatment of vibrations in harmonic approximation.
Abstract: The authors extend their recent method for the computation of vibrationally resolved optical spectra of large molecules, including both the Duschinsky rotation and the effect of finite temperature in the framework of the Franck-Condon (FC) approximation, to deal with the more general case of the Herzberg-Teller (HT) model, where also the linear dependence of the transition dipole moment on the nuclear coordinates is taken into account. This generalization allows us to investigate weak and vibronically allowed transitions by far extending the range of application of the method. The calculation of the spectra of sizable molecules is computationally demanding because of the huge number of final vibrational states that must be taken into account, and the inclusion of HT terms further increases the computational burden. The method presented here automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a modest computational requirement. The effectiveness of the method is illustrated by computing the HT absorption and fluorescence Q(x) spectra of free-base porphyrin both at T=0 K and at room temperature, performing for the first time an exact treatment of vibrations in harmonic approximation. Q(x) spectra are compared to experiments and FC/HT interferences are analyzed in detail.
TL;DR: Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules.
Abstract: Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole moments are computed using the same geometries (MP2/6-31G∗) and basis set (TZVP) as in our previous ab initio benchmark study on electronically excited states. The results from TD-DFT (with the functionals BP86, B3LYP, and BHLYP) and from DFT/MRCI are compared against the previous high-level ab initio results, and, in particular, against the proposed best estimates for 104 singlet and 63 triplet vertical excitation energies. The statistical evaluation for the latter reference data gives the lowest mean absolute deviations for DFT/MRCI (0.22 eV for singlets and 0.24 eV for triplets) followed by TD-DFT/B3LYP (0.27 and 0.44 eV, respectively), whereas TD-DFT/BP86 and TD-DFT/BHLYP are significantly less accurate. The ene...
TL;DR: These findings show the limited predictive power of these theoretical methods to describe the electronic structure of reduced titania in the absence of accurate experimental data.
Abstract: The removal of lattice O atoms, as well as the addition of interstitial H atoms, in TiO(2) is known to cause the reduction in the material and the formation of "Ti(3+)" ions. By means of electronic structure calculations we have studied the nature of such oxygen vacancy and hydrogen impurity states in the bulk of the anatase polymorph of TiO(2). The spin polarized nature of these centers, the localized or delocalized character of the extra electrons, the presence of defect-induced states in the gap, and the polaronic distortion around the defect have been investigated with different theoretical methods: standard density functional theory (DFT) in the generalized-gradient approximation (GGA), GGA+U methods as a function of the U parameter, and two hybrid functionals with different admixtures of Hartree-Fock exchange. The results are found to be strongly dependent on the method used. Only GGA+U or hybrid functionals are able to reproduce the presence of states at about 1 eV below the conduction band, which are experimentally observed in reduced titania. The corresponding electronic states are localized on Ti 3d levels, but partly delocalized solutions are very close in energy. These findings show the limited predictive power of these theoretical methods to describe the electronic structure of reduced titania in the absence of accurate experimental data.
TL;DR: The results demonstrate that the peak in the parallel-polarized Raman spectrum at about 3250 wavenumbers is collective in nature, and shows that while the coupling between chromophores is relatively modest, it nevertheless produces delocalization of the vibrational eigenstates over up to 12 Chromophores, which has a profound effect on the spectroscopy.
Abstract: IR and Raman (parallel- and perpendicular-polarized) spectra in the OH stretch region for liquid water were measured some years ago, but their interpretation is still controversial. In part, this is because theoretical calculation of such spectra for a neat liquid presents a formidable challenge due to the coupling between vibrational chromophores and the effects of motional narrowing. Recently we proposed an electronic structure/molecular dynamics method for calculating spectra of dilute HOD in liquid D(2)O, which relied on ab initio calculations on clusters to provide a map from nuclear coordinates of the molecules in the liquid to OH stretch frequencies, transition dipoles, and polarizabilities. Here we extend this approach to the calculation of couplings between chromophores. From the trajectories of the fluctuating local-mode frequencies, transition moments, and couplings, we use our recently developed time-averaging approximation to calculate the line shapes. Our results are in good agreement with experiment for the IR and Raman line shapes, and capture the significant differences among them. Our analysis shows that while the coupling between chromophores is relatively modest, it nevertheless produces delocalization of the vibrational eigenstates over up to 12 chromophores, which has a profound effect on the spectroscopy. In particular, our results demonstrate that the peak in the parallel-polarized Raman spectrum at about 3250 wavenumbers is collective in nature.
TL;DR: These new auxiliary basis sets have been optimized for the elements H, B-Ne, and Al-Ar, and result in very small RI errors, as exemplified by the calculated atomization energies of 42 molecules at the MP2-F12 level.
Abstract: Auxiliary basis sets for use in explicitly correlated MP2-F12 and CCSD-F12 methods, in which three- and four-electron integrals are approximated as products of two-electron integrals through the resolution of the identity (RI), have been optimized for the elements H, B–Ne, and Al–Ar. Fully matched to the recently constructed cc-pVnZ-F12 orbital basis sets, these new auxiliary basis sets result in very small RI errors, as exemplified by the calculated atomization energies of 42 molecules at the MP2-F12 level. Their utility in calculating smooth potential energy surfaces is also demonstrated in calculations of the spectroscopic properties of several diatomic molecules.
TL;DR: A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described, and applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented.
Abstract: A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described. This model is particularly effective for cases where a chemical system requires a balanced orbital active space that is too large to be addressed by the complete active space self-consistent field model with or without second-order perturbation theory (CASPT2 or CASSCF, respectively). Rather than permitting all possible electronic configurations of the electrons in the active space to appear in the reference wave function, certain orbitals are sequestered into two subspaces that permit a maximum number of occupations or holes, respectively, in any given configuration, thereby reducing the total number of possible configurations. Subsequent second-order perturbation theory captures additional dynamical correlation effects. Applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented. In the mononuclear case, RASPT2 and CASPT2 provide very similar results. In the binuclear cases, however, only RASPT2 proves quantitatively useful, owing to the very large size of the necessary active space.
TL;DR: While in traditional fluorescence resonance energy transfer, the rate has a (distance)(-6) dependence, it is found that the distance dependence in this case is quite different, and the calculation of rate in the case of the two dyes, pyrene and nile blue, shows that thedistance dependence is Yukawa type.
Abstract: We study the distance dependence of the rate of resonance energy transfer from the excited state of a dye to the \pi system of graphene. Using the tight-binding model for the \pi system and the Diraccone approximation, we obtain the analytic expression for the rate of energy transfer from an
electronically excited dye to graphene. While in traditional fluorescence resonance energy transfer, the rate has a $(distance)^{-6}$ dependence, we find that the distance dependence in this case is quite different. Our calculation of rate in the case of the two dyes, pyrene and nile blue, shows that the distance dependence is Yukawa type. We have also studied the effect of doping on energy transfer to graphene. Doping does not modify the rate for electronic excitation energy transfer significantly. However, in the case of vibrational transfer, the rate is found to be increased by an order of magnitude due to doping. This can be attributed to the nonzero density of states at the Fermi level that results from doping.
TL;DR: Fortuitous cancellation of high-level effects is shown to give the overall HEAT strategy an accuracy that is, in fact, higher than most of its individual components.
Abstract: Effects of increased basis-set size as well as a correlated treatment of the diagonal Born-Oppenheimer approximation are studied within the context of the high-accuracy extrapolated ab initio thermochemistry (HEAT) theoretical model chemistry. It is found that the addition of these ostensible improvements does little to increase the overall accuracy of HEAT for the determination of molecular atomization energies. Fortuitous cancellation of high-level effects is shown to give the overall HEAT strategy an accuracy that is, in fact, higher than most of its individual components. In addition, the issue of core-valence electron correlation separation is explored; it is found that approximate additive treatments of the two effects have limitations that are significant in the realm of <1kJmol−1 theoretical thermochemistry.
TL;DR: The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.
Abstract: A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantu...
TL;DR: The new model is able to produce results of similar quality with the previous versions for the structures and energetics of water clusters as well as structural and thermodynamic properties of liquid water evaluated with classical and converged quantum statistical mechanical atomistic simulations.
Abstract: We present a new parametrization of the flexible, polarizable Thole-type model for water [J. Chem. Phys. 116, 5115 (2002); J. Phys. Chem. A 110, 4100 (2006)], with emphasis in describing the vibrational spectra of both water clusters and liquid water. The new model is able to produce results of similar quality with the previous versions for the structures and energetics of water clusters as well as structural and thermodynamic properties of liquid water evaluated with classical and converged quantum statistical mechanical atomistic simulations. At the same time it yields accurate redshifts for the OH vibrational stretches of both water clusters and liquid water.
TL;DR: A multilayer extension of the correlation discrete variable representation (CDVR) scheme employed in MCTDH calculations studying quantum dynamics on general potential energy surfaces is developed and tested in a simple numerical application and might offer a perspective to rigorously describe the quantum dynamics of larger polyatomic systems.
Abstract: The multiconfigurational time-dependent Hartree (MCTDH) approach facilitates multidimensional quantum dynamics calculations by representing the wavepacket in an optimal set of time-dependent basis functions, called single-particle functions Choosing these single-particle functions to be themselves multidimensional wavefunctions which are represented using a MCTDH representation, a multilayer MCTDH scheme has been constructed and used for quantum dynamics calculations treating up to 1000 degrees of freedom rigorously [Wang and Thoss, J Chem Phys 199, 1289 (2003)] The present work gives a practical scheme which facilitates the application of the multilayer MCTDH approach, which previously has only been employed to study systems described by model-type Hamiltonians, to molecular systems described by more complicated Hamiltonians and general potential energy surfaces A multilayer extension of the correlation discrete variable representation (CDVR) scheme employed in MCTDH calculations studying quantum dynamics on general potential energy surfaces is developed and tested in a simple numerical application The resulting multilayer MCTDH/CDVR approach might offer a perspective to rigorously describe the quantum dynamics of larger polyatomic systems
TL;DR: This work describes in detail how this daubechies wavelets basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations.
Abstract: Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances, and an excellent efficiency for parallel calculations.
TL;DR: The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF.
Abstract: The multiscale coarse-graining MS-CG method S. Izvekov and G.A. Voth, J. Phys. Chem. B 109, 2469 2005; J. Chem. Phys. 123, 134105 2005 employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force PMF governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM + /NO 3 ionic liquid are provided to illustrate the method. © 2008 American
TL;DR: A survey of the widely varying magnitude of the most important components contributing to the atomization energies and structures of 106 small molecules is presented, which combines large Gaussian basis sets and coupled cluster theory up to quadruple excitations for all systems.
Abstract: High level electronic structure predictions of thermochemical properties and molecular structure are capable of accuracy rivaling the very best experimental measurements as a result of rapid advances in hardware, software, and methodology. Despite the progress, real world limitations require practical approaches designed for handling general chemical systems that rely on composite strategies in which a single, intractable calculation is replaced by a series of smaller calculations. As typically implemented, these approaches produce a final, or “best,” estimate that is constructed from one major component, fine-tuned by multiple corrections that are assumed to be additive. Though individually much smaller than the original, unmanageable computational problem, these corrections are nonetheless extremely costly. This study presents a survey of the widely varying magnitude of the most important components contributing to the atomization energies and structures of 106 small molecules. It combines large Gaussia...
TL;DR: The resulting DMRG-CASSCF method is used to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as beta-carotene, correlating with near-exact accuracy the optimized complete pi-valence space with up to 24 active electrons and orbitals.
Abstract: In previous work we have shown that the density matrix renormalization group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional complete active space algorithms. Here, we implement orbital optimization with the DMRG to further allow the self-consistent improvement of the active orbitals, as is done in the complete active space self-consistent field (CASSCF) method. We use our resulting DMRG-CASSCF method to study the low-lying excited states of the all-trans polyenes up to C_(24)H_(26) as well as β-carotene, correlating with near-exact accuracy the optimized complete π-valence space with up to 24 active electrons and orbitals, and analyze our results in the light of the recent discovery from resonance Raman experiments of new optically dark states in the spectrum.
TL;DR: In this paper, the authors present benchmark calculations using several long-range-corrected LRC density functionals, in which Hartree-Fock exchange is incorporated asymptotically using a range-separated Coulomb operator, while local exchange is attenuated using an ansatz introduced by Iikura et al.
Abstract: We present benchmark calculations using several long-range-corrected LRC density functionals, in which Hartree–Fock exchange is incorporated asymptotically using a range-separated Coulomb operator, while local exchange is attenuated using an ansatz introduced by Iikura et al. J. Chem. Phys. 115, 3540 2001. We calculate ground-state atomization energies, reaction barriers, ionization energies, and electron affinities, each as a function of the range-separation parameter . In addition, we calculate excitation energies of small- and medium-sized molecules, again as a function of , by applying the LRC to time-dependent density functional theory. Representative examples of both pure and hybrid density functionals are tested. On the basis of these results, there does not appear to be a single range-separation parameter that is reasonable for both ground-state properties and vertical excitation energies. Reasonable errors in atomization energies and barrier heights are achieved only at the expense of excessively high excitation energies, at least for the medium-sized molecules, whereas values of that afford reasonable excitation energies yield some of the largest errors for ground-state atomization energies and barrier heights in small molecules. Notably, this conclusion is obscured if the database of excitation energies includes only small molecules, as has been the case in previous benchmark studies of LRC functionals. © 2008 American Institute of Physics. DOI: 10.1063/1.2954017
TL;DR: Numerical tests show that quantum coherence can cause significant changes in steady state donor/acceptor populations from those predicted by the FD theory and illustrate delicate cooperation of nonequilibrium and quantum coherent effects on the transient population dynamics.
Abstract: A theory of coherent resonance energy transfer is developed combining the polaron transformation and a time-local quantum master equation formulation, which is valid for arbitrary spectral densities including common modes. The theory contains inhomogeneous terms accounting for nonequilibrium initial preparation effects and elucidates how quantum coherence and nonequilibrium effects manifest themselves in the coherent energy transfer dynamics beyond the weak resonance coupling limit of the Forster and Dexter (FD) theory. Numerical tests show that quantum coherence can cause significant changes in steady state donor/acceptor populations from those predicted by the FD theory and illustrate delicate cooperation of nonequilibrium and quantum coherence effects on the transient population dynamics.
TL;DR: The new technique employs a relationship between U and J and the Coulomb and exchange integrals evaluated using the entire set of UHF molecular orbitals (MOs) for the system, eliminating the difficulty in selecting unambiguously the MOs that correspond to localized states.
Abstract: Conventional density functional theory (DFT) fails for strongly correlated electron systems due to large intra-atomic self-interaction errors. The DFT+U method provides a means of overcoming these errors through the use of a parametrized potential that employs an exact treatment of quantum mechanical exchange interactions. The parameters that enter into this potential correspond to the spherically averaged intra-atomic Coulomb (U) and exchange (J) interactions. Recently, we developed an ab initio approach for evaluating these parameters on the basis of unrestricted Hartree-Fock (UHF) theory, which has the advantage of being free of self-interaction errors and does not require experimental input [Mosey and Carter, Phys. Rev. B 76, 155123 (2007)]. In this work, we build on that method to develop a more robust and convenient ab initio approach for evaluating U and J. The new technique employs a relationship between U and J and the Coulomb and exchange integrals evaluated using the entire set of UHF molecular orbitals (MOs) for the system. Employing the entire set of UHF MOs renders the method rotationally invariant and eliminates the difficulty in selecting unambiguously the MOs that correspond to localized states. These aspects overcome two significant deficiencies of our earlier method. The new technique is used to evaluate U and J for Cr(2)O(3), FeO, and Fe(2)O(3). The resulting values of U-J are close to empirical estimates of this quantity for each of these materials and are also similar to results of constrained DFT calculations. DFT+U calculations using the ab initio parameters yield results that are in good agreement with experiment. As such, this method offers a means of performing accurate and fully predictive DFT+U calculations of strongly correlated electron materials.