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Accurate low-order structure factors (Fg) measured by quantitative convergent beam electron diffraction (QCBED) were used for validation of different density functional theory (DFT) approximations. Twenty-three low-order Fg were measured for the transition metals Cr, Fe, Co, Ni, and Cu, and the transition metal based intermetallic phases γ-TiAl, β-NiAl, and γ1-FePd using a multi-beam off-zone axis QCBED method and then compared with Fg calculated by ab initio DFT using the local density approximation (LDA) and LDA + U, and different generalized gradient approximations (GGA) functionals. Different functionals perform very differently for different materials and crystal structures regarding prediction of low-order Fg. All the GGA functionals tested in the paper except for EV93 achieve good overall agreement with the experimentally determined low-order Fg for BCC Cr and Fe, while EV93 performs the best for FCC Ni and Cu. The LDA and GGA functional fail to predict accurately the low-order Fg for β-NiAl and γ1-FePd. The LDA + U approach, through tuning of U, can achieve excellent matches with the experimentally measured Fg for all the metallic systems investigated in this paper. The use of experimentally accessible low order Fg as an additional set of metrics in approaches of validation of DFT calculations is discussed and has potential to assist in and to stimulate development of improved functionals. [ABSTRACT FROM AUTHOR]

In an earlier paper [S. Thanos and A. K. Theophilou J. Chem. Phys. 124, 204109 (2006)], we found an explicit formula for the expansion of a Slater determinant |[uppercase_phi_synonym]M> in terms of eigenstates of S2. In this paper, we use the same formula to determine the spin contamination Scon of the unrestricted single determinant approximations, i.e., Hartree-Fock, optimized effective potential, and density functional theory. We derived an expression which gives Scon in terms of the overlap of the spatial parts of the spin up and spin down “corresponding” orbitals. It was found that Scon does not depend on M, the eigenvalue of Sz, at least for the lower order approximations, i.e., when |<φi|φi′>| is large. In this case, the predominant coefficient of the expansion assumes its maximum value when S=M. However, for the class of solutions that |<φi|φi′>| is small, the spin L of the largest coefficient increases with the number of unpaired electrons. We also derived the explicit form of the expansion states. [ABSTRACT FROM AUTHOR]

This paper generalizes the recently proposed approaches for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) based on a Slater transition-state density to transitions such as singlet-singlet excitations, where a single-determinant ansatz is insufficient. The proposed approach is based on restricted open-shell Frank et al. [J. Chem. Phys. 108, 4060 (1998)] theory used to describe a spin-adapted Slater transition state. To treat the dependence of electron-electron interactions on the nuclear positions, variational linear-response density-functional perturbation theory is generalized to reference states with an orbital-dependent Kohn-Sham Hamiltonian and nontrivial occupation patterns. The methods proposed in this paper are not limited to the calculation of derivative coupling vectors, but can also be used for the calculation of other transition matrix elements. Moreover, they can be used to calculate the linear response of open-shell systems to arbitrary external perturbations in DFT. [ABSTRACT FROM AUTHOR]

Explicitly time-dependent density functional theory (TDDFT) is a formally exact theory, which can treat very large systems. However, in practice it is used almost exclusively in the adiabatic approximation and with standard ground state functionals. Therefore, if combined with coherent control theory, it is not clear which control tasks can be achieved reliably, and how this depends on the functionals. In this paper, we continue earlier work in order to establish rules that answer these questions. Specifically, we look at the creation of wave packets by ultrashort laser pulses that contain several excited states. We find that (i) adiabatic TDDFT only works if the system is not driven too far from the ground state, (ii) the permanent dipole moments involved should not differ too much, and (iii) these results are independent of the functional used. Additionally, we find an artifact that produces fluence-dependent excitation energies. [ABSTRACT FROM AUTHOR]

This paper assesses the accuracy of the ΔSCF method for computing low-lying HOMO→LUMO transitions in organic dye molecules. For a test set of vertical excitation energies of 16 chromophores, surprisingly similar accuracy is observed for time-dependent density functional theory and for ΔSCF density functional theory. In light of this performance, we reconsider the ad hoc ΔSCF prescription and demonstrate that it formally obtains the exact stationary density within the adiabatic approximation, partially justifying its use. The relative merits and future prospects of ΔSCF for simulating individual excited states are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced 'chain of spheres exchange' (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ∼26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ∼27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ∼24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ∼15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system. [ABSTRACT FROM AUTHOR]

Recently, the use of polarizable force fields in Molecular Dynamics simulations has been gaining importance, since they allow a better description of heterogeneous systems compared to simple point charges force fields. Among the various techniques developed in the last years the one based on polarizable point dipoles represents one of the most used. In this paper, we review the basic technical issues of the method, illustrating the way to implement intramolecular and intermolecular damping of the electrostatic interactions, either with and without the Ewald summation method. We also show how to reduce the computational overhead for evaluating the dipoles, introducing to the state-of-the-art methods: the extended Lagrangian method and the always stable predictor corrector method. Finally we discuss the importance of screening the electrostatic interactions at short range, defending this technique against simpler approximations usually made. We compare results of density functional theory and classical force field-based Molecular Dynamics simulations of chloride in water. [ABSTRACT FROM AUTHOR]

In this paper, a quasirelativistic two-component zeroth order regular approximation (ZORA) density functional theory (DFT) approach to the calculation of parity violating (PV) resonance frequency differences between the nuclear magnetic resonance (NMR) spectra of enantiomers is presented and the systematics of PV NMR shielding constants in C2-symmetric dihydrogen dichalcogenides (H2X2 with X=17O, 33S, 77Se, 125Te, 209Po) are investigated. The typical sin(2α)-like dependence of the PV NMR frequency splittings on the dihedral angle α is observed for the entire series. As for the scaling behavior of the effect with the nuclear charge Z of X, the previously reported Z2.5±0.5 scaling in the nonrelativistic limit is reproduced and a scaling of approximately Z3 for the paramagnetic and Z5 for the spin-orbit coupling contribution to the frequency splitting is observed in the relativistic framework. The paramagnetic and spin-orbit coupling contributions are typically of opposite sign for the molecular structures studied herein and the maximum scaling of the total ZORA frequency splitting (i.e., the sum of the two contributions) is Z3.9 for H2Po2. Thus, an earlier claim for a spin-orbit coupling contribution scaling with up to Z7 for H2Po2 and the erratic dihedral angle dependence obtained for this compound within a four-component Dirac–Hartree–Fock–Coulomb study is not confirmed at the DFT level. The maximum NMR frequency splitting reported here is of the order of 10 mHz for certain clamped conformations of H2Po2 inside a static magnetic field with magnetic flux density of 11.7 T. Frequency splittings of this size have been estimated to be detectable with present day NMR spectrometers. Thus, a NMR route toward molecular PV appears promising once suitable compounds have been identified. [ABSTRACT FROM AUTHOR]

This paper presents a detailed theoretical analysis of the electronic structure of the CsFe[Cr(CN)6] prussian blue analog with emphasis on the structural origin of the experimentally observed spin crossover transition in this material. Periodic density functional calculations using generalized gradient approximation (GGA)+U and nonlocal hybrid exchange-correlation potentials show that, for the experimental low temperature crystal structure, the t2g6eg0 low spin configuration of FeII is the most stable and CrIII (S=3/2, t2g3eg0) remains the same in all cases. This is also found to be the case for the low spin GGA+U fully relaxed structure with the optimized unit cell. A completely different situation emerges when calculations are carried out using the experimental high temperature structure. Here, GGA+U and hybrid density functional theory calculations consistently predict that the t2g4eg2 FeII high spin configuration is the ground state. However, the two spin configurations appear to be nearly degenerate when calculations are carried out for the geometries arising from a GGA+U full relaxation of the atomic structure carried out at experimental high temperature lattice constant. A detailed analysis of the energy difference between the two spin configurations as a function of the lattice constant strongly suggests that the observed spin crossover transition has a structural origin with non-negligible entropic contributions of the high spin state. [ABSTRACT FROM AUTHOR]

Finding the underlying mechanism from the statistical properties of an experimental two-state trajectory generated from dynamics in a complex on-off multisubstate kinetic scheme (KS) is the aim of many experiments. Since the data explicitly shows only transitions between substates of different states, information about the KS is lost, resulting in equivalence of KSs, i.e., the occurrence of different KSs that lead to the same data, in a statistical sense. In order to deal with this phenomenon, a canonical (unique) form of reduced dimensions (RD) is built from the data. RD forms are on-off networks with connections only between substates of different states, where the connections usually have nonexponential waiting time probability density functions. In this paper, we give a list of (about 50) relationships between properties of the data, the topology of reduced dimension forms, and features of KSs. Many of these relationships involve symmetries in RD forms, KSs, and the data and irreversible transitions in KSs. These relationships are useful both in theoretical analysis of on-off KSs and in the analysis of the data. [ABSTRACT FROM AUTHOR]

In this paper, double ionization energies (DIEs) of gas-phase atoms and molecules are calculated by energy difference method with density functional theory. To determine the best functional for double ionization energies, we first study 24 main group atoms in the second, third, and fourth periods. An approximation is used in which the electron density is first obtained from a density functional computation with the exchange-correlation potential Vxc known as statistical average of orbital potentials, after which the energy is computed from that density with 59 different exchange-correlation energy functionals Exc. For the 24 atoms, the two best Exc functional providing DIEs with average absolute deviation (AAD) of only 0.25 eV are the Perdew–Burke–Ernzerhof functional modified by Hammer et al. [Phys. Rev. B 59, 6413 (1999)] and one known as the Krieger–Chen–Iafrate–Savin functional modified by Krieger et al. (unpublished). Surprisingly, none of the 20 available hybrid functionals is among the top 15 functionals for the DIEs of the 24 atoms. A similar procedure is then applied to molecules, with opposite results: Only hybrid functionals are among the top 15 functionals for a selection of 29 molecules. The best Exc functional for the 29 molecules is found to be the Becke 1997 functional modified by Wilson et al. [J. Chem. Phys. 115, 9233 (2001)]. With that functional, the AAD from experiment for DIEs of 29 molecules is just under 0.5 eV. If the two suspected values for C2H2 and Fe(CO)5 are excluded, the AAD improves to 0.32 eV. Many other hybrid functionals perform almost as well. [ABSTRACT FROM AUTHOR]

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Mo\ller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods. [ABSTRACT FROM AUTHOR]

Semilocal density functional approximations (DFAs) for the exchange-correlation energy suffer from self-interaction error, which is believed to be the cause of many of the failures of common DFAs, such as poor description of charge transfer and transition states of chemical reactions. The standard self-interaction correction (SIC) of Perdew and Zunger mends some of these failures but spoils such essential properties as thermochemistry and equilibrium bond lengths. The Perdew-Zunger SIC seems to overcorrect many-electron systems. In this paper, we propose a modified SIC, which is scaled down in many-electron regions. The new SIC has an improved performance for many molecular properties, including total energies, atomization energies, barrier heights of chemical reactions, ionization potentials, electron affinities, and bond lengths. The local spin-density approximation (LSDA) benefits from SIC more than higher-level functionals do. The scaled-down SIC has only one adjustable parameter. Rationalization of the optimal value of this parameter enables us to construct an almost-nonempirical version of the scaled-down SIC-LSDA, which is significantly better than uncorrected LSDA and even better than the uncorrected generalized gradient approximation. We present an analysis of the formal properties of the scaled-down SIC and define possible directions for further improvements. In particular, we find that exactness for all one-electron densities does not guarantee correct asymptotics for the exchange-correlation potential of a many-electron system. [ABSTRACT FROM AUTHOR]

The five points of criticism in Wesolowski's comment can be separated into three categories. Two issues are related to the question whether the nonadditive kinetic-energy functional or its functional derivative should be investigated, which is a matter of personal choice of research subject. Another issue is an unfounded accusation addressing the numerical soundness of our data. Finally, the remaining two points do not concern our paper, but deal with connections between previous work by two of us [J. Chem. Phys. 126, 234116 (2007)] and by Wesolowski and co-workers [J. Chem. Phys.129, 074107 (2008)], which we clarify in this response. Issues from all three categories have in common that they do not question the usefulness of our paper, or criticize any of our results or conclusions. [ABSTRACT FROM AUTHOR]

Transport properties of molecular junctions are notoriously expensive to calculate with ab initio methods, primarily due to the semi-infinite electrodes. This has led to the introduction of different approximation schemes for the electrodes. For the most popular metals used in experiments, such as gold, the wide-band limit (WBL) is a particularly efficient choice. In this paper, we investigate the performance of different WBL schemes relative to more sophisticated approaches including the fully self-consistent non-equilibrium Green's function method. We find reasonably good agreement between all schemes for systems in which the molecule (and not the metal-molecule interface) dominates the transport properties. Moreover, our implementation of the WBL requires negligible computational effort compared to the ground-state density-functional theory calculation of a molecular junction. We also present a new approximate but efficient scheme for calculating transport with a finite bias. Provided the voltage drop occurs primarily inside the molecule, this method provides results in reasonable agreement with fully self-consistent calculations. [ABSTRACT FROM AUTHOR]

The key characteristics of electronic excitations of many-electron systems, the excitation energies ωα and the oscillator strengths fα, can be obtained from linear response theory. In one-electron models and within the adiabatic approximation, the zeros of the inverse response matrix, which occur at the excitation energies, can be obtained from a simple diagonalization. Particular cases are the eigenvalue equations of time-dependent density functional theory (TDDFT), time-dependent density matrix functional theory, and the recently developed phase-including natural orbital (PINO) functional theory. In this paper, an expression for the oscillator strengths fα of the electronic excitations is derived within adiabatic response PINO theory. The fα are expressed through the eigenvectors of the PINO inverse response matrix and the dipole integrals. They are calculated with the phase-including natural orbital functional for two-electron systems adapted from the work of Lowdin and Shull on two-electron systems (the phase-including Löwdin-Shull functional). The PINO calculations reproduce the reference fα values for all considered excitations and bond distances R of the prototype molecules H2 and HeH+ very well (perfectly, if the correct choice of the phases in the functional is made). Remarkably, the quality is still very good when the response matrices are severely restricted to almost TDDFT size, i.e., involving in addition to the occupied-virtual orbital pairs just (HOMO+1)-virtual pairs (R1) and possibly (HOMO+2)-virtual pairs (R2). The shape of the curves fα(R) is rationalized with a decomposition analysis of the transition dipole moments. [ABSTRACT FROM AUTHOR]

We recently proposed a linear-scaling evaluation scheme for the second-order Mo\ller-Plesset perturbation (MP2) energy based on the divide-and-conquer (DC) method [M. Kobayashi, Y. Imamura, and H. Nakai, J. Chem. Phys. 127, 074103 (2007)]. In this paper, we propose an approximate but effective expression for the first derivative of the DC-MP2 energy. The present scheme evaluates the one- and two-body density matrices, which appear in the MP2 gradient formula, in the DC manner; that is, the entire matrix is obtained as the sum of subsystem matrices masked by the partition matrix. Therefore, the method requires solving only the local Z-vector equations. Illustrative applications to three types of systems, peptides, Si surface model, and delocalized polyenes, reveal the effectiveness of the present method. [ABSTRACT FROM AUTHOR]