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The non-Markovian approach developed in the companion paper [Hughes et al., J. Chem. Phys. 131, 024109 (2009)], which employs a hierarchical series of approximate spectral densities, is extended to the treatment of nonadiabatic dynamics of coupled electronic states. We focus on a spin-boson-type Hamiltonian including a subset of system vibrational modes which are treated without any approximation, while a set of bath modes is transformed to a chain of effective modes and treated in a reduced-dimensional space. Only the first member of the chain is coupled to the electronic subsystem. The chain construction can be truncated at successive orders and is terminated by a Markovian closure acting on the end of the chain. From this Mori-type construction, a hierarchy of approximate spectral densities is obtained which approach the true bath spectral density with increasing accuracy. Applications are presented for the dynamics of a vibronic subsystem comprising a high-frequency mode and interacting with a low-frequency bath. The bath is shown to have a striking effect on the nonadiabatic dynamics, which can be rationalized in the effective-mode picture. A reduced two-dimensional subspace is constructed which accounts for the essential features of the nonadiabatic process induced by the effective environmental mode. Electronic coherence is found to be preserved on the shortest time scale determined by the effective mode, while decoherence sets in on a longer time scale. Numerical simulations are carried out using either an explicit wave function representation of the system and overall bath or else an explicit representation of the system and effective-mode part in conjunction with a Caldeira–Leggett master equation. [ABSTRACT FROM AUTHOR]

This paper is the first of a two-part series dealing with quantum-mechanical (density-functional-based) studies of helium-mediated deposition of catalytic species on the rutile TiO2(110)-(1×1) surface. The interaction of helium with the TiO2(110)-(1×1) surface is first evaluated using the Perdew-Burke-Ernzerhof functional at a numerical grid dense enough to build an analytical three-dimensional potential energy surface. Three (two prototype) potential models for the He-surface interaction in helium scattering calculations are analyzed to build the analytical potential energy surface: (1) the hard-corrugated-wall potential model; (2) the corrugated-Morse potential model; and (3) the three-dimensional Morse potential model. Different model potentials are then used to study the dynamics upon collision of a 4He300 cluster with the TiO2(110) surface at zero temperature within the framework of a time-dependent density-functional approach for the quantum fluid [D. Mateo, D. Jin, M. Barranco, and M. Pi, J. Chem. Phys. 134, 044507 (2011)] and classical dynamics calculations. The laterally averaged density functional theory-based potential with an added long-range dispersion interaction term is further applied. At variance with classical dynamics calculations, showing helium droplet splashing out of the surface at impact, the time evolution of the macroscopic helium wave-function predicts that the helium droplet spreads on the rutile surface and leads to the formation of a thin film above the substrate. This work thus provides a basis for simulating helium mediated deposition of metallic clusters embedded within helium nanodroplets. [ABSTRACT FROM AUTHOR]

Biomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs self-consistently during the calculation of the density. We have implemented this scheme in a linear-scaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species. [ABSTRACT FROM AUTHOR]

In this paper we perform a systematic investigation on all-trans polyacetylene chains of different lengths, end-capped with moieties of different donor or acceptor natures and different strengths, to infer useful structure/property relationship rules and behavioral patterns. The values for bond length alternation (BLA), longitudinal polarizability, and first and second hyperpolarizabilities have been computed with the Coulomb-attenuating density function (CAM-B3LYP), using response theory. A comparison of the relative effect that each end-capping combination contributes to BLA, linear, and nonlinear optical coefficients has been performed. This results in useful insights and general rules to ad hoc tailoring the molecular response for a specific characteristic. [ABSTRACT FROM AUTHOR]

Multicomponent density functional theory has been developed to treat systems with more than one type of quantum particle, such as electrons and nuclei, in an external potential. The existence of the exact universal multicomponent density functional in terms of the one-particle densities for each type of quantum particle has been proven. In the present paper, a number of important mathematical properties of the exact universal multicomponent density functional are derived. The expression relating the electron-proton pair density to the one-particle densities leads to an inequality for the potential energy component of the electron-proton correlation functional under well-defined conditions. General inequalities for the kinetic energy correlation functionals and the total electron-proton correlation functional are also derived. The coordinate scaling analysis leads to mathematical inequalities describing the effect of scaled densities on the kinetic, potential, and total energy functionals. The adiabatic connection formula defines the exact electron-proton functional in terms of an adiabatic scaling parameter that smoothly connects the noninteracting system with the fully interacting system. The virial expression provides the relation between the exact kinetic and potential energy functionals for the ground state densities of multicomponent systems. These mathematical relationships provide insight into the fundamental properties of the exact universal multicomponent density functional and serve as a guide for the development of approximate electron-proton density functionals. [ABSTRACT FROM AUTHOR]

This paper describes the development of the B3LYP localized orbital correction model which improves the accuracy of the B3LYP thermochemical predictions for compounds containing transition metals. The development of this model employs a large data set containing 36 experimental atomic energies and 71 bond dissociation energies. B3LYP calculations were carried out on these systems with different basis sets. Based on an electronic structure analysis and physical arguments, we built a set of 10 parameters to correct atomic data and a set of 21 parameters to correct bond dissociation energies. Using the results from our biggest basis set, the model was shown to reduce the mean absolute deviation from 7.7 to 0.4 kcal/mol for the atomic data and from 5.3 to 1.7 kcal/mol for the bond dissociation energies. The model was also tested using a second basis set and was shown to give relatively accurate results too. The model was also able to predict an outlier in the experimental data that was further investigated with high level coupled-cluster calculations. [ABSTRACT FROM AUTHOR]

A new method called adaptive force matching (AFM) has been developed that is capable of producing high quality force fields for condensed phase simulations. This procedure involves the parametrization of force fields to reproduce ab initio forces obtained from condensed phase quantum-mechanics/molecular-mechanics (QM/MM) calculations. During the procedure, the MM part of the QM/MM is iteratively improved so as to approach ab initio quality. In this work, the AFM method has been tested to parametrize force fields for liquid water so that the resulting force fields reproduce forces calculated using the ab initio MP2 and the Kohn–Sham density functional theory with the Becke–Lee–Yang–Parr (BLYP) and Becke three-parameter LYP (B3LYP) exchange correlation functionals. The AFM force fields generated in this work are very simple to evaluate and are supported by most molecular dynamics (MD) codes. At the same time, the quality of the forces predicted by the AFM force fields rivals that of very expensive ab initio calculations and are found to successfully reproduce many experimental properties. The site-site radial distribution functions (RDFs) obtained from MD simulations using the force field generated from the BLYP functional through AFM compare favorably with the previously published RDFs from Car–Parrinello MD simulations with the same functional. Technical aspects of AFM such as the optimal QM cluster size, optimal basis set, and optimal QM method to be used with the AFM procedure are discussed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we solve quantum many-body problem by propagating ensembles of trajectories and guiding waves in physical space. We introduce the “effective potential” correction within the recently proposed time-dependent quantum Monte Carlo methodology to incorporate the nonlocal quantum correlation effects between the electrons. The associated correlation length is calculated by adaptive kernel density estimation over the walker distribution. The general formalism is developed and tested on one-dimensional helium atom in laser field of different intensities and carrier frequencies. Good agreement with exact results for the atomic ionization is obtained. [ABSTRACT FROM AUTHOR]

Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb’s Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the υ-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the v- and N-representability problems based on the constrained search formalism. [ABSTRACT FROM AUTHOR]

In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term vp of completely kinetic origin. Virial theorem and hierarchy of equations are derived for vp and simple approximations are proposed. A relationship between the effective potential up of the shape function equation and the potential vp is established. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

For large reactive systems, the calculation of energies can be simplified by treating the active part with a high-level quantum mechanical (QM) (ab initio or density functional) approach and the environment with a less sophisticated semiempirical (SE) approach, as an improvement over the widely used hybrid quantum mechanical/molecular mechanical (QM/MM) methods. An example is the interaction between an active region of an enzyme and its immediate environment. One such method is the original "Our-own-N-layer Integrated molecular Orbital+Molecular Mechanics (ONIOM)" approach. In this paper, the interaction between the QM and SE region is described explicitly by two different schemes. In the iterative QM/SE schemes (QM/SE-I), the electrostatic interaction and polarization effects are introduced explicitly for both the QM and SE atoms by a self-consistent procedure based on either polarizable point charges or the electron density. In the noniterative QM/SE scheme, based on the ONIOM model (QM/SE-O), the exchange (Pauli repulsion) and charge transfer effects are taken into account at the SE level, in addition to the explicit electrostatic interaction and polarization between the two regions. Test calculations are made on a number of model systems (including small polar or charged molecules interacting with water and proton transfer reactions in the presence of polar molecules or an extended hydrogen-bond network). The quantitative accuracy of the results depend on several parameters, such as the charge-scaling/normalization factors for the SE charge and the QM/SE van der Waals parameters, which can be chosen to optimize the result. For the QM/SE-O approach, the results are more sensitive to the quality of the SE level (e.g., self-consistent-charge density-functional-tight-binding vs AMl) than the explicit interaction between QM and SE atoms. [ABSTRACT FROM AUTHOR]

Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw–Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficient and viscosity of aluminum at 116 045 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods. [ABSTRACT FROM AUTHOR]

We perform spin-polarized density functional theory calculations for a hydrogen atom interacting exohedrally with a (5,5) single-walled carbon nanotube (SWNT). We also perform full three-dimensional (3D) quantum dynamics calculations of the H atom bound rovibrational states. We initially focus on the four sites of highest symmetry, along which we compute potential energy surface (PES) values at 33 separate, nonuniformly spaced radial values. These 132 geometries are sufficient to define the primary potential interaction regions. We find a weak physisorptive region between 2.5 and 3.5 Å from the SWNT wall, with a maximum well depth of 51 meV, relative to the desorption limit. We also find a chemisorptive region, extending from about 1.0 out to 1.5 Å from the SWNT wall. The maximum well depth of 0.755 eV occurs at 1.15 Å from the SWNT wall, nearly directly above a carbon atom. A small barrier of 54 meV lies between these two binding regions. There are also two types of transition states that lie between adjacent chemisorption wells. In addition to the high-symmetry sites, a detailed and accurate characterization of the PES requires density functional theory calculations along a large number of interstitial sites—18 in all. Using these 18×33 geometries, and exploiting the full D10h symmetry of the system, we fit a global analytical PES, using a Fourier basis in the cylindrical coordinates, with radially dependent expansion coefficients (rms error 3.8 meV). We then perform a mixed spectral basis/phase-space optimized discrete variable representation calculation of all bound rovibrational H atom eigenfunctions and energy levels. We also discuss ramifications for the possible use of SWNTs as hydrogen storage devices. [ABSTRACT FROM AUTHOR]

In the ground state, the pair density n can be determined by solving a single auxiliary equation of a two-particle problem. Electron-electron cusp condition and asymptotic behavior for the Pauli potential of the effective potential of the two-particle equation are presented. [ABSTRACT FROM AUTHOR]

We provide a rigorous proof that the Hohenberg-Kohn theorem holds for spin densities by extending Lieb’s Legendre-transform formulation to spin densities. The resulting spin-density-functional theory resolves several troublesome issues. Most importantly, the present paper provides an explicit construction for the spin potentials at any point along the adiabatic connection curve, thus providing a formal basis for the use of exchange-correlation functionals of the spin density in the Kohn-Sham density-functional theory (DFT). The practical implications of this result for unrestricted Kohn-Sham DFT calculations is considered, and the existence of holes below the Fermi level is discussed. We argue that an orbital’s energy tends to increase as its occupation number increases, which provides the basis for a computational algorithm for determining the occupation numbers in Kohn-Sham DFT and helps explain the origin of Hund’s rules and holes below the Fermi level. [ABSTRACT FROM AUTHOR]

We report the details of a theory which predicts the freezing of quantum liquids, such as helium [J. Chem. Phys. 90, 4622 (1989)]. The freezing of a wide variety of classical liquids has been described by the density functional (DF) theory of statistical mechanics. By choosing a new ideal system, we construct a new DF theory which addresses directly many of the unusual features of the freezing of liquid helium, such as the weakly modulated liquid pair correlation function g(r) at freezing densities. The theory combines DF techniques with the Feynman path integral formulation of quantum mechanics, to include correctly dispersion effects. In classical DF theories, the density and external field of the ideal system are connected by a Boltzmann relation ρ(r)∝exp[-βV(r)]. In our quantum DF theory, we relate the density and external field of the ideal system through the Feynman path integral representation, in which the quantum particle is represented by a classical ‘‘ring polymer’’ of P beads. In practical applications, the DF perturbation expansion is truncated at second order, and classical DF theories fail for helium because they employ an ideal system which is too far removed from the interacting system. For a certain simplified problem, the density path integral of the ideal system can be performed in closed form, leading to a compact, physically descriptive theory. In a companion paper, the full theory is applied to the freezing of helium-4 and yields good results. [ABSTRACT FROM AUTHOR]

The concept of local pressure in an electronic system is extended and developed, starting from an integral relation of Bartolotti and Parr (Ref. 11) and using the local thermodynamic language of Ghosh, Berkowitz, and Parr (GBP) (Ref. 3), who have shown that for an ideal, noninteracting microscopic system the internal pressure at a point r is purely kinetic and given by ps=ρ(r)kT(r), where T(r) is an appropriately defined local temperature. In the present paper, we show that this equation, exact for the noninteracting, ideal system within the local thermodynamic transcription is a first order truncation of the real, interacting system pressure density functional, which contains explicit correlation and exchange pressure contributions, which act as ‘‘deviations from ideality’’ in the real system. From analogy with the macroscopic situation, the pressure density functional is written as a virial expansion in terms of the density. [ABSTRACT FROM AUTHOR]

It is a well recognized difficult task to simulate the vibrational dynamics of ices using the density functional theory (DFT), and there has thus been rather limited success in modelling the inelastic neutron scattering (INS) spectra for even the simplest structure of ice, ice Ih, particularly in the translational region below 400 cm-1. The reason is partly due to the complex nature of hydrogen bonding (H-bond) among water-water molecules which require considerable improvement of the quantum mechanical simulation methods, and partly owing to the randomness of protons in ice structures which often requires simulation of large super-lattices. In this report, we present the first series of successful simulation results for ice Ih using DFT methods. On the basis of the recent advancement in the DFT programs, we have achieved for the first time theoretical outcomes that not only reproduce the rotational frequencies between 500 to 1200 cm-1 for ice Ih, but also the two optic peaks at ∼240 and 320 cm-1 in the translational region of the INS spectra [J. C. Li, J. Chem. Phys 105, 6733 (1996)]. Besides, we have also investigated the impact of pairwise configurations of H2O molecules on the H-bond and found that different proton arrangements of pairwise H2O in the ice Ih crystal lattice could not alter the nature of H-bond as significantly as suggested in an early paper [J. C. Li and D. K. Ross, Nature (London) 365, 327 (1993)], i.e., reproducing the two experimental optic peaks do not need to invoke the two H-bonds as proposed in the previous model which led to considerable debates. The results of this work suggest that the observed optic peaks may be attributed to the coupling between the two bands of H-O stretching modes in H2O. The current computational work is expected to shed new light on the nature of the H-bonds in water, and in addition to offer a new approach towards probing the interaction between water and biomaterials for which H-bond is essential. [ABSTRACT FROM AUTHOR]

The interplay between electron-electron and electron-proton correlation is investigated within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT) approach, which treats electrons and select protons quantum mechanically on the same level. Recently two electron-proton correlation functionals were developed from the electron-proton pair densities obtained from explicitly correlated wavefunctions. In these previous derivations, the kinetic energy contribution arising from electron-proton correlation was neglected. In this paper, an electron-proton correlation functional that includes this kinetic energy contribution is derived using the adiabatic connection formula in multicomponent DFT. The performance of the NEO-DFT approach using all three electron-proton correlation functionals in conjunction with three well-established electronic exchange-correlation functionals is assessed. NEO-DFT calculations with these electron-proton correlation functionals capture the increase in the hydrogen vibrational stretching frequencies arising from the inclusion of electron-electron correlation in model systems. Electron-proton and electron-electron correlation are found to be uncoupled and predominantly additive effects to the total energy for the model systems studied. Thus, electron-proton correlation functionals and electronic exchange-correlation functionals can be developed independently and subsequently combined together without re-parameterization. [ABSTRACT FROM AUTHOR]

Very accurate non-Born-Oppenheimer quantum-mechanical calculations are performed to determine the average values of the interparticle distances and the proton-deuteron density function for the rovibrationally excited HD+ ion. The states corresponding to excitations to all bound vibrational states (v = 0, ..., 22) and simultaneously excited to the first excited rotational state (N = 1) are considered. To describe each state up to 8000 explicitly correlated all-particle Gaussian functions are used. The nonlinear parameters of the Gaussians are variationally optimized using a procedure that employs the analytical energy gradient determined with respect to these parameters. The results show an increasing asymmetry in the electron distribution with the vibrational excitation as the electron density shifts towards deuteron and away from the proton. [ABSTRACT FROM AUTHOR]

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G0, the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G0. We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the fractional charge. It should play an important role in developing accurate approximate density functionals and many-body theory. [ABSTRACT FROM AUTHOR]

In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state. [ABSTRACT FROM AUTHOR]

Fully quantum-mechanical treatment of the effects of thermal rovibrational motion in a heavy-element molecule with relativistic effects is carried out for the heavy 129/131Xe and light 19F nuclear shieldings in the linear XeF2 molecule. More importantly, purely quantum-mechanical, intramolecular phenomena, the primary and secondary isotope effect on these shieldings, respectively, are treated with including both the zero-point vibrational and finite-temperature effects. While large solvent effects influence the experimental absolute shielding constants and chemical shifts (thereby making comparison of experiment and theory very difficult), they are not significant for the isotope shifts. We study the role of electron correlation at both nonrelativistic (NR) and relativistic [Breit-Pauli perturbational theory (BPPT) as well as 4-component Dirac theory] level. We obtain quantitative agreement with the nearly solvent-independent experimental 19F secondary isotope shifts. This implies a promising accuracy for our predictions of the experimentally so far non-existing primary Xe isotope shift and the temperature dependence of Xe and F chemical shifts corresponding to a low pressure gas phase. To achieve this, a combination of high-level ab initio NR shielding surface is found necessary, in the present work supplemented by relativistic corrections by density-functional theory (DFT). Large errors are demonstrated to arise due to DFT in the NR shielding surface, explaining findings in recent computational studies of heavy-element isotope shifts. Besides a high-quality property hypersurface, the inclusion of thermal effects (in addition to zero-point motion) is also necessary to compare with experimental results. The geometry dependence of the different relativistic influences on the wave function, Zeeman interaction, and hyperfine interaction, as well as their role in the temperature dependence of both the Xe and F shielding constants and their isotope shifts, are discussed. The relativistic rovibrational effects arise from the same individual contributions as previously found for the chemical shifts and shielding anisotropies. In general, the spin-orbit interactions are more sensitive to rovibrational motion than the scalar relativistic contributions. A previously suggested third-order BPPT contribution to shielding anisotropy is shown to be important for a better agreement with experiment. [ABSTRACT FROM AUTHOR]

Using quantum mechanics (QM) and classical force-field based molecular dynamics (FF), we have calculated the principle shock Hugoniot curves for numerous amorphous polymers including poly[methyl methacrylate] (PMMA), poly[styrene], polycarbonate, as well as both the amorphous and crystalline forms of poly[ethylene]. In the FF calculations, we considered a non-reactive force field (i.e., polymer consistent FF). The QM calculations were performed with density functional theory (DFT) using dispersion corrected atom centered pseudopotentials. Overall, results obtained by DFT show much better agreement with available experimental data than classical force fields. In particular, DFT calculated Hugoniot curves for PMMA up to 74 GPa are in very good agreement with experimental data, where a preliminary study of chain fracture and association was also performed. Structure analysis calculations of the radius of gyration and carbon-carbon radial distribution function were also carried out to elucidate contraction of the polymer chains with increasing pressure. [ABSTRACT FROM AUTHOR]

Octahedral Fe2+ molecules are particularly interesting as they often exhibit a spin-crossover transition. In spite of the many efforts aimed at assessing the performances of density functional theory for such systems, an exchange-correlation functional able to account accurately for the energetic of the various possible spin-states has not been identified yet. Here, we critically discuss the issues related to the theoretical description of this class of molecules from first principles. In particular, we present a comparison between different density functionals for four ions, namely, [Fe(H2O)6]2+, [Fe(NH3)6]2+, [Fe(NCH)6]2+, and [Fe(CO)6]2+. These are characterized by different ligand-field splittings and ground state spin multiplicities. Since no experimental data are available for the gas phase, the density functional theory results are benchmarked against those obtained with diffusion Monte Carlo, one of the most accurate methods available to compute ground state total energies of quantum systems. On the one hand, we show that most of the functionals considered provide a good description of the geometry and of the shape of the potential energy surfaces. On the other hand, the same functionals fail badly in predicting the energy differences between the various spin states. In the case of [Fe(H2O)6]2+, [Fe(NH3)6]2+, [Fe(NCH)6]2+, this failure is related to the drastic underestimation of the exchange energy. Therefore, quite accurate results can be achieved with hybrid functionals including about 50% of Hartree-Fock exchange. In contrast, in the case of [Fe(CO)6]2+, the failure is likely to be caused by the multiconfigurational character of the ground state wave-function and no suitable exchange and correlation functional has been identified. [ABSTRACT FROM AUTHOR]

Effect of electron correlation on single strand breaks (SSBs) induced by low energy electron (LEE) has been investigated in a fragment excised from a DNA, viz., 2′-deoxycytidine-3′-monophosphate [3′-dCMPH] molecule in gas phase at DFT-B3LYP/6-31+G(d) accuracy level and using local complex potential based time dependent wave packet (LCP-TDWP) approach. The results obtained, in conjunction with our earlier investigation, show the possibility of SSB at very low energy (0.15 eV) where the LEE transfers from π* to σ* resonance state which resembles a SN2 type mechanism. In addition, for the first time, an indication of quantum mechanical tunneling in strand breaking is seen from the highest anionic bound vibrational state (χ5), which may have a substantial role during DNA damage. [ABSTRACT FROM AUTHOR]

Using quantum molecular dynamics simulations based on density functional theory including dispersion corrections (DFT-D), we have studied the thermophysical properties of liquid carbon monoxide and nitrogen (CO-N2) mixture under extreme conditions. Density functional theory (DFT) method significantly overestimates the pressure as compared to DFT-D. It is demonstrated that the van der Waals (vdW) interaction has a negative contribution to the pressure and tends to reduce the overestimation of the equilibrium volume. We also demonstrate that a negative slope of Hugoniot curve could possibly be caused by both the absorption of dissociation energy and the uncertainties in composition. As density and temperature increase along the Hoguniot curve, the system appears to undergo a continuous transition and provides for a much richer set of dissociation products. The influence of dissociated carbon and oxygen atoms on nitrogen molecules is also discussed. [ABSTRACT FROM AUTHOR]

We present a detailed study of the energetics of water clusters (H2O)n with n <= 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water. [ABSTRACT FROM AUTHOR]

In an effort to design efficient platform for siRNA delivery, we combine all atom classical and quantum simulations to study the binding of small interfering RNA (siRNA) by pristine single wall carbon nanotube (SWCNT). Our results show that siRNA strongly binds to SWCNT surface via unzipping its base-pairs and the propensity of unzipping increases with the increase in the diameter of the SWCNTs. The unzipping and subsequent wrapping events are initiated and driven by van der Waals interactions between the aromatic rings of siRNA nucleobases and the SWCNT surface. However, molecular dynamics (MD) simulations of double strand DNA (dsDNA) of the same sequence show that the dsDNA undergoes much less unzipping and wrapping on the SWCNT in the simulation time scale of 70 ns. This interesting difference is due to smaller interaction energy of thymidine of dsDNA with the SWCNT compared to that of uridine of siRNA, as calculated by dispersion corrected density functional theory (DFT) methods. After the optimal binding of siRNA to SWCNT, the complex is very stable which serves as one of the major mechanisms of siRNA delivery for biomedical applications. Since siRNA has to undergo unwinding process with the effect of RNA-induced silencing complex, our proposed delivery mechanism by SWCNT possesses potential advantages in achieving RNA interference. [ABSTRACT FROM AUTHOR]

The physisorption of molecular hydrogen in model carbon foams has been investigated from 50 K to room temperature. The study is carried out within the framework of the density functional theory for quantum liquids at finite temperatures. Calculations are performed in the grand canonical ensemble, i.e., the adsorbed fluid is assumed to be in equilibrium with an external gas of hydrogen molecules with concentrations ranging from 8×10-4 kg m-3 to n=71 kg m-3. It is shown that, while strong zero-point energy effects are present even at room temperature, the adsorption isotherms exhibit only a weak dependence on the explicit incorporation of the bosonic exchange symmetry of hydrogen molecules. The increase of the average particle density prevents the deviations from the Maxwell-Boltzmann statistics to become noticeable if the system is cooled down. The volumetric storage capacity of these materials at low temperatures is about one half of the U. S. Department of Energy goal, while the gravimetric capacity is still far from the standards required by mobile applications. The relation between the microscopic structure of the hydrogen fluid and the calculated adsorption properties is also addressed. [ABSTRACT FROM AUTHOR]

A time-dependent wavepacket diffusion method is proposed to deal with charge transport in organic crystals. The electron-phonon interactions in both site energies and electronic couplings are incorporated by the time-dependent fluctuations which are generated from the corresponding spectral density functions. The numerical demonstrations reveal that the present approach predicts the consistent charge carrier dynamics with the rigorous quantum approaches. In addition, the diffusion coefficients obtained from the Marcus formula are well reproduced at the weak electronic coupling and high temperature limits. It is also found that the charge mobility feature of the crossover from the band-like to the hopping-type cannot be predicted from the fluctuations induced by the linear electron-phonon interactions with an Ohmic spectral density; however, it indeed appears as the electronic coupling fluctuation exponentially depends on the nuclear coordinates. Finally, it should be noted that although the present approach neglects the imaginary fluctuation, it essentially incorporates the coherent motion of the charge carrier and quantum effect of the phonon motion with a broad regime of the fluctuations for symmetric systems. Besides, the approach can easily be applied to systems having thousands of sites, which allows one to investigate charge transport in nanoscale organic crystals. [ABSTRACT FROM AUTHOR]

A first principles quantum mechanical calculation of the vibrational energy levels and transition frequencies associated with protons in stoichiometric LiNbO3 single crystal has been carried out. The hydrogen contaminated crystal has been approximated by a model one obtains by translating a supercell, i.e., a cluster of LiNbO3 unit cells containing a single H+ and a Li+ vacancy. Based on the supercell model an approximate Hamiltonian operator describing vibrations of the proton sublattice embedded in the host crystal has been derived. It is further simplified to a sum of uncoupled Hamiltonian operators corresponding to different wave vectors (ks) and each describing vibrations of a quasi-particle (quasi-proton). The three dimensional (3D) Hamiltonian operator of k=0 has been employed to calculate vibrational levels and transition frequencies. The potential energy surface (PES) entering this Hamiltonian operator has been calculated point wise on a large set of grid points by using density functional theory, and an analytical approximation to the PES has been constructed by non-parametric approximation. Then, the nuclear motion Schrödinger equation has been solved by employing the method of discrete variable representation. It has been found that the (quasi-)H+ vibrates in a strongly anharmonic PES. Its vibrations can be described approximately as a stretching, and two orthogonal bending vibrations. The theoretically calculated transition frequencies agree within 1% with those experimentally determined, and they have allowed the assignment of one of the hitherto unassigned bands as a combination of the stretching and the bending of lower fundamental frequency. [ABSTRACT FROM AUTHOR]

We present a method which uses the results of a molecular Kohn-Sham calculation at a reference geometry to approximate the energy at many different geometries. The Kohn-Sham electron density of the reference geometry is decomposed into atomic fragments, which move with the nuclei to approximate the density at a new geometry and the energy is evaluated with the Harris-Foulkes functional. Preliminary results for a biological quantum-mechanics/molecular-mechanics trajectory are promising: the errors of reference-geometry Harris-Foulkes (compared to full self-consistent Kohn-Sham) for the PBE exchange-correlation functional have the same magnitude as the difference between the energies of PBE and BLYP. [ABSTRACT FROM AUTHOR]

For a rigorous quantum simulation of nonadiabatic dynamics of electrons and nuclei, knowledge of not only the first-order but also the second-order nonadiabatic couplings (NACs) is required. Here, we propose a method to efficiently calculate the second-order NAC from time-dependent density functional theory (TDDFT), on the basis of the Casida ansatz adapted for the computation of first-order NAC, which has been justified in our previous work and can be shown to be valid for calculating second-order NAC between ground state and singly excited states within the Tamm-Dancoff approximation. Test calculations of the second-order NAC in the immediate vicinity of Jahn-Teller and Renner-Teller intersections show that calculation results from TDDFT, combined with modified linear response theory, agree well with the prediction from the Jahn-Teller/Renner-Teller models. Contrary to the diverging behavior of the first-order NAC near all types of intersection points, the Cartesian components of the second-order NAC are shown to be negligibly small near Renner-Teller glancing intersections, while they are significantly large near the Jahn-Teller conical intersections. Nevertheless, the components of the second-order NAC can cancel each other to a large extent in Jahn-Teller systems, indicating the background of neglecting the second-order NAC in practical dynamics simulations. On the other hand, it is shown that such a cancellation becomes less effective in an elliptic Jahn-Teller system and thus the role of second-order NAC needs to be evaluated in the rigorous framework. Our study shows that TDDFT is promising to provide accurate data of NAC for full quantum mechanical simulation of nonadiabatic processes. [ABSTRACT FROM AUTHOR]

We present a combination of time-dependent density functional theory with the quantum mechanical/molecular mechanical approach which can be applied to study nonadiabatic dynamical processes in molecular systems interacting with the environment. Our method is illustrated on the example of ultrafast excited state dynamics of indole in water. We compare the mechanisms of nonradiative relaxation and the electronic state lifetimes for isolated indole, indole in a sphere of classical water, and indole + 3H2O embedded in a classical water sphere. In the case of isolated indole, the initial excitation to the S2 electronic state is followed by an ultrafast internal conversion to the S1 state with a time constant of 17 fs. The S1 state is long living (>30 ps) and deactivates to the ground state along the N-H stretching coordinate. This deactivation mechanism remains unchanged for indole in a classical water sphere. However, the lifetimes of the S2 and S1 electronic states are extended. The inclusion of three explicit water molecules opens a new relaxation channel which involves the electron transfer to the solvent, leading eventually to the formation of a solvated electron. The relaxation to the ground state takes place on a time scale of 60 fs and contributes to the lowering of the fluorescence quantum yield. Our simulations demonstrate the importance of including explicit water molecules in the theoretical treatment of solvated systems. [ABSTRACT FROM AUTHOR]

A systematic and unbiased structure search based on a genetic algorithm in combination with density functional theory (DFT) procedures has been carried out to locate low-energy isomers of Gan up to n = 25. For the smaller clusters up to n = 8 results are checked by coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) employing a quadruple zeta type basis set. The CCSD(T) calculations confirm a 3Πu ground state for the dimer. Ga3 has a doublet ground state 0.2 eV below two quartet states, whereas two isoenergetic triplet states are predicted for Ga4 with D4h and a rhombus structure (D2h). Three low-lying isomers with doublet electronic states are found for Ga5: a W-structure (C2v), a planar envelope (Cs) at 0.015 eV, and a non-planar envelope (C1) 0.086 eV above the ground state. A triplet state for a trigonal prism (D3h) and a singlet for an open prism (C2v) are computed with virtually identical energy for Ga6. The global minimum for Ga7 is a capped trigonal prism (Cs) and that for Ga8 a distorted cube in D2h. DFT provides a fair agreement with CCSD(T), deviations in dissociation energies are up to 0.2 eV for n <= 8. The structures for Gan are mostly irregular for n >= 9, those for Ga12 to Ga17 can be derived from the truncated decahedron with D5h symmetry though highly distorted by Jahn-Teller effects, for example. For Ga18 to Ga23 we find stacks of five- and six-membered rings as global minima, e.g., 5-1-5-1-6 for Ga18. Ga24 and Ga25 consist of layers with packing sequence ABCBA similar to those found for clusters of aluminum. The most important feature of computed cohesive energies is a rapid increase with n: for Ga25 it reaches 2.46 eV, the experimental bulk value is 2.84 eV. Particularly stable clusters for Gan are seen for n = 7, 14, and 20. [ABSTRACT FROM AUTHOR]

A study on static polarizabilities for a family of gold clusters (Aun, n = 6, 12, 20, 34, 54) is presented. For each cluster, a density functional theory perturbation theory calculation was performed to compute the cluster polarizability and the polarizability of each atom in the cluster using Baders 'quantum theory of atoms in molecules' formalism. The cluster polarizability tensor, αcluster, is expressed as a sum of the atom-in-molecule tensors, αcluster=∑Ωα(Ω). A strong quadratic correlation (R2 = 0.98) in the isotropic polarizability of atoms in the cluster and their distance to the cluster center of mass was observed. The cluster polarizabilities are in agreement with previous calculations. [ABSTRACT FROM AUTHOR]

Near edge x-ray absorption fine structure (NEXAFS) spectra at the boron K-edge were measured for aqueous boric acid, borate, and polyborate ions, using liquid microjet technology, and compared with simulated spectra calculated from first principles density functional theory in the excited electron and core hole (XCH) approximation. Thermal motion in both hydrated and isolated molecules was incorporated into the calculations by sampling trajectories from quantum mechanics/molecular mechanics simulations at the experimental temperature. The boron oxide molecules exhibit little spectral change upon hydration, relative to mineral samples. Simulations reveal that water is arranged nearly isotropically around boric acid and sodium borate, but the calculations also indicate that the boron K-edge NEXAFS spectra are insensitive to hydrogen bonding, molecular environment, or salt interactions. [ABSTRACT FROM AUTHOR]

Starting from the equation of motion in the density matrix formulation, we reformulate the analytical gradient of the excited-state energy at the time-dependent density functional theory level in the nonorthogonal Gaussian atom-centered orbital (AO) basis. Analogous to the analytical first derivative in molecular-orbital (MO) basis, a Z-vector equation has been derived with respect to the reduced one-electronic density matrix in AO basis, which provides a potential possibility to exploit quantum locality of the density matrix and avoids the matrix transformation between the AO and the MO basis. Numerical tests are finished for the excited-state geometry optimization and adiabatic excitation energy calculation of a series of small molecules. The results demonstrate the computational efficiency and accuracy of the current AO-based energy gradient expression in comparison with the MO-based scheme. [ABSTRACT FROM AUTHOR]

We study the performance of two different electrode models in quantum transport calculations based on density functional theory: parametrized Bethe lattices and quasi-one-dimensional wires or nanowires. A detailed account of implementation details in both the cases is given. From the systematic study of nanocontacts made of representative metallic elements, we can conclude that the parametrized electrode models represent an excellent compromise between computational cost and electronic structure definition as long as the aim is to compare with experiments where the precise atomic structure of the electrodes is not relevant or defined with precision. The results obtained using parametrized Bethe lattices are essentially similar to the ones obtained with quasi-one-dimensional electrodes for large enough cross-sections of these, adding a natural smearing to the transmission curves that mimics the true nature of polycrystalline electrodes. The latter are more demanding from the computational point of view, but present the advantage of expanding the range of applicability of transport calculations to situations where the electrodes have a well-defined atomic structure, as is the case for carbon nanotubes, graphene nanoribbons, or semiconducting nanowires. All the analysis is done with the help of codes developed by the authors which can be found in the quantum transport toolbox ALACANT and are publicly available. [ABSTRACT FROM AUTHOR]

We have studied substituent effects on the properties of the intramolecular hydrogen bond of some ortho-hydroxy Schiff bases using density functional theory (DFT) based first-principle molecular dynamics (FPMD) and path integral molecular dynamics. The studied compounds possess a strong intramolecular hydrogen bond (r(O···N) ≤ 2.6 Å), which can be tuned by substitution to either (i) enhance the basicity of the acceptor moiety by induction effects or (ii) decrease the hydrogen bond length through steric repulsion. DFT calculations and FPMD were employed to investigate structural and dynamical properties of the selected molecules, while quantum effects on the structural properties were assessed using path integral FPMD. The simulations were performed in vacuo and in the solid state to study the influence of the environment on the hydrogen bond and spectroscopic properties. We give computational support to the suggestion that induction effects are less effective to tune the intramolecular hydrogen bond properties of the discussed ortho-hydroxy Schiff bases than the steric or the environmental effects. [ABSTRACT FROM AUTHOR]

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|Hab|2>)1/2=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |Hab|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level. [ABSTRACT FROM AUTHOR]

Recently, we have proposed a scheme for the calculation of nonadiabatic couplings and nonadiabatic coupling vectors within linear response time-dependent density functional theory using a set of auxiliary many-electron wavefunctions [I. Tavernelli, E. Tapavicza, and U. Rothlisberger, J. Chem. Phys. 130, 124107 (2009)]. As demonstrated in a later work [I. Tavernelli, B. F. E. Curchod, and U. Rothlisberger, J. Chem. Phys. 131, 196101 (2009)], this approach is rigorous in the case of the calculation of nonadiabatic couplings between the ground state and any excited state. In this work, we extend this formalism to the case of coupling between pairs of singly excited states with the same spin multiplicity. After proving the correctness of our formalism using the electronic oscillator approach by Mukamel and co-workers [S. Tretiak and S. Mukamel, Chem. Rev. (Washington, D.C.) 102, 3171 (2002)], we tested the method on a model system, namely, protonated formaldimine, for which we computed S1/S2 nonadiabatic coupling vectors and compared them with results from high level (MR-CISD) electronic structure calculations. [ABSTRACT FROM AUTHOR]

Schofield's form of quantum time correlation functions is used as the starting point to derive a computable expression for these quantities. The time composition property of the propagators in complex time is exploited to approximate Schofield's function in terms of a sequence of short time classical propagations interspersed with path integrals that, combined, represent the thermal density of the system. The approximation amounts to linearization of the real time propagators and it becomes exact with increasing number of propagation legs. Within this scheme, the correlation function is interpreted as an expectation value over a probability density defined on the thermal and real path space and calculated by a Monte Carlo algorithm. The performance of the algorithm is tested on a set of benchmark problems. Although the numerical effort required is considerable, we show that the algorithm converges systematically to the exact answer with increasing number of iterations and that it is stable for times longer than those accessible via a brute force, path integral based, calculation of the correlation function. Scaling of the algorithm with dimensionality is also examined and, when the method is combined with commonly used filtering schemes, found to be comparable to that of alternative semiclassical methods. [ABSTRACT FROM AUTHOR]

We describe an ab initio approach to compute the optical absorption spectra of molecules and solids, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator. This procedure is equivalent to solving the statically screened Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on density functional perturbation theory. In this way, full absorption spectra may be obtained with a computational workload comparable to ground state Hartree-Fock calculations. We present results for small molecules, for the spectra of a 1 nm Si cluster in a wide energy range (20 eV), and for a dipeptide exhibiting charge transfer excitations. [ABSTRACT FROM AUTHOR]

The effects of the reactant bending excitations in the F+CHD3 reaction are investigated by crossed molecular beam experiments and quasiclassical trajectory (QCT) calculations using a high-quality ab initio potential energy surface. The collision energy (Ec) dependence of the cross sections of the F+CHD3(vb=0,1) reactions for the correlated product pairs HF(v′)+CD3(v2=0,1) and DF(v′)+CHD2(v4=0,1) is obtained. Both experiment and theory show that the bending excitation activates the reaction at low Ec and begins to inactivate at higher Ec. The experimental F+CHD3(vb=1) excitation functions display surprising peak features, especially for the HF(v′=3)+CD3(v2=0,1) channels, indicating reactive resonances (quantum effects), which cannot be captured by quasiclassical calculations. The reactant state-specific QCT calculations predict that the v5(e) bending mode excitation is the most efficient to drive the reaction and the v6(e) and v5(e) modes enhance the DF and HF channels, respectively. [ABSTRACT FROM AUTHOR]

As assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of the graphene planes (thus graphite falls apart into graphene sheets). To provide a basis for describing these London interactions, we derive the quantum mechanics based force field for carbon (QMFF-Cx) by fitting to results from density functional theory calculations at the M06-2X level, which demonstrates accuracies for a broad class of molecules at short and medium range intermolecular distances. We carried out calculations on the dehydrogenated coronene (C24) dimer, emphasizing two geometries: parallel-displaced X (close to the observed structure in graphite crystal) and PD-Y (the lowest energy transition state for sliding graphene sheets with respect to each other). A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads to accurate predictions of available experimental mechanical and thermodynamics data of graphite (lattice vibrations, elastic constants, Poisson ratios, lattice modes, phonon dispersion curves, specific heat, and thermal expansion). This validates the use of M06-2X as a practical method for development of new first principles based generations of QMFF force fields. [ABSTRACT FROM AUTHOR]

The frozen-density embedding (FDE) scheme [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] relies on the use of approximations for the kinetic-energy component vT[ρ1,ρ2] of the embedding potential. While with approximations derived from generalized-gradient approximation kinetic-energy density functional weak interactions between subsystems such as hydrogen bonds can be described rather accurately, these approximations break down for bonds with a covalent character. Thus, to be able to directly apply the FDE scheme to subsystems connected by covalent bonds, improved approximations to vT are needed. As a first step toward this goal, we have implemented a method for the numerical calculation of accurate references for vT. We present accurate embedding potentials for a selected set of model systems, in which the subsystems are connected by hydrogen bonds of various strength (water dimer and F–H–F-), a coordination bond (ammonia borane), and a prototypical covalent bond (ethane). These accurate potentials are analyzed and compared to those obtained from popular kinetic-energy density functionals. [ABSTRACT FROM AUTHOR]

In Hohenberg–Kohn density functional theory, the energy E is expressed as a unique functional of the ground state density ρ(r): E=E[ρ] with the internal energy component FHK[ρ] being universal. Knowledge of the functional FHK[ρ] by itself, however, is insufficient to obtain the energy: the particle number N is primary. By emphasizing this primacy, the energy E is written as a nonuniversal functional of N and probability density p(r): E=E[N,p]. The set of functions p(r) satisfies the constraints of normalization to unity and non-negativity, exists for each N;N=1,...,∞, and defines the probability density or p-space. A particle number N and probability density p(r) functional theory is constructed. Two examples for which the exact energy functionals E[N,p] are known are provided. The concept of A-representability is introduced, by which it is meant the set of functions Ψp that leads to probability densities p(r) obtained as the quantum-mechanical expectation of the probability density operator, and which satisfies the above constraints. We show that the set of functions p(r) of p-space is equivalent to the A-representable probability density set. We also show via the Harriman and Gilbert constructions that the A-representable and N-representable probability density p(r) sets are equivalent. [ABSTRACT FROM AUTHOR]

Using a recently implemented technique for the calculation of the adiabatic connection (AC) of density functional theory (DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and molecules containing up to ten electrons: the helium isoelectronic series, the hydrogen molecule, the beryllium isoelectronic series, the neon atom, and the water molecule. The calculation of AC curves by Lieb maximization at various levels of electronic-structure theory is discussed. For each system, the AC curve is calculated using Hartree–Fock (HF) theory, second-order Mo\ller–Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, expanding the molecular orbitals and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlation-energy contribution in the context of DFT, arising from orbital relaxation as the electron-electron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doubles-energy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple two-parameter doubles model (AC-D) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triples-energy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (AC-T). From a consideration of the structure of a two-level configuration-interaction (CI) energy expression of the hydrogen molecule, a simple two-parameter CI model (AC-CI) is proposed to account for the effects of static correlation on the AC. When parametrized in terms of the same input data, the AC-CI model offers improved performance over the corresponding AC-D model, which is shown to be the lowest-order contribution to the AC-CI model. The utility of the accurately calculated AC curves for the analysis of standard density functionals is demonstrated for the BLYP exchange-correlation functional and the interaction-strength-interpolation (ISI) model AC integrand. From the results of this analysis, we investigate the performance of our proposed two-parameter AC-D and AC-CI models when a simple density functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting two-parameter correlation functionals offer a qualitatively correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here. [ABSTRACT FROM AUTHOR]