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The objective of this paper is to show that the density fitting (resolution of the identity approximation) can also be applied to Coulomb integrals of the type (k1(1)k2(1)|g1(2)g2(2)), where k and g symbols refer to plane-wave functions and gaussians, respectively. We have shown how to achieve the accuracy of these integrals that is needed in wave-function MO and density functional theory-type calculations using mixed Gaussian and plane-wave basis sets. The crucial issues for achieving such a high accuracy are application of constraints for conservation of the number electrons and components of the dipole moment, optimization of the auxiliary basis set, and elimination of round-off errors in the matrix inversion. [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 proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In the foregoing Comment [Sommerfeld[J. Chem. Phys.125, 024307 (2006)] suggests that the computational results presented in the above referenced paper does not support the conclusion of the paper regarding the prevalence of both surface- and interior-bound electron states for (H2O)14- clusters in experiments. Herein, the author presents the method used in the selection of clusters and provide experimental results that are consistent with the findings of the paper. [ABSTRACT FROM AUTHOR]

For chemistry an accurate description of bond weakening and breaking is vital. The great advantage of density matrix functionals, as opposed to density functionals, is their ability to describe such processes since they naturally cover both nondynamical and dynamical correlation. This is obvious in the Löwdin-Shull functional, the exact natural orbital functional for two-electron systems. We present in this paper extensions of this functional for the breaking of a single electron pair bond in N-electron molecules, using LiH, BeH+, and Li2 molecules as prototypes. Attention is given to the proper formulation of the functional in terms of not just J and K integrals but also the two-electron L integrals (K integrals with a different distribution of the complex conjugation of the orbitals), which is crucial for the calculation of response functions. Accurate energy curves are obtained with extended Löwdin-Shull functionals along the complete dissociation coordinate using full CI calculations as benchmark. [ABSTRACT FROM AUTHOR]

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms. [ABSTRACT FROM AUTHOR]

In this paper we evaluate the performance of density functional theory with the B3LYP functional for calculations on ceria (CeO2) and cerium sesquioxide (Ce2O3). We demonstrate that B3LYP is able to describe CeO2 and Ce2O3 reasonably well. When compared to other functionals, B3LYP performs slightly better than the hybrid functional PBE0 for the electronic properties but slightly worse for the structural properties, although neither performs as well as LDA+U(U=6 eV) or PBE+U(U=5 eV). We also make an extensive comparison of atomic basis sets suitable for periodic calculations of these cerium oxides. Here we conclude that there is currently only one type of cerium basis set available in the literature that is able to give a reasonable description of the electronic structure of both CeO2 and Ce2O3. These basis sets are based on a 28 electron effective core potential (ECP) and 30 electrons are attributed to the valence space of cerium. Basis sets based on 46 electron ECPs fail for these materials. [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]

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]

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e., the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating “memory” effects: the derived exchange-correlation potential will depend not only on present densities but also on the past. In order to ensure the potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn–Sham equations. The exchange-correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal exchange-correlation vector potential for the Kohn–Sham equations incorporating memory effects. We show explicitly that the net exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit). © 2004 American Institute of Physics. [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]

Gas-phase hydrogen atoms are accelerated towards metallic surfaces in their vicinity. As it approaches the surface, the velocity of an atom increases and this motion excites the metallic electrons, causing energy loss to the atom. This dissipative dynamics is frequently described as atomic motion under friction, where the friction coefficient is obtained from ab initio calculations assuming a weak interaction and slow atom. This paper tests the aforementioned approach by comparing to a real-time Ehrenfest molecular dynamics simulation of such a process. The electrons are treated realistically using standard approximations to time-dependent density functional theory. We find indeed that the electronic excitations produce a frictionlike force on the atom. However, the friction coefficient strongly depends on the direction of the motion of the atom: it is large when the atom is moving towards the cluster and much smaller when the atom is moving away. It is concluded that a revision of the model for energy dissipation at metallic surfaces, at least for clusters, may be necessary. [ABSTRACT FROM AUTHOR]

In this paper we further develop the formalism of tunneling currents for thesssssss description of the tunneling transition in long-distance bridge-mediated electron transfer reactions introduced in our previous work [A. A. Stuchebrukhov, Adv. Chem. Phys. 118, 1 (2001)]. Here we consider the Hartree-Fock picture of electron tunneling in a many-electron system and, based on the corresponding orbitals analysis of the tunneling process, we introduce an effective one-electron approximation. In this picture, the (electron or hole) tunneling is described by a single pair of orbitals, as in a true one-electron theory, yet all the polarization and exchange effects characteristic for many-electron treatment are retained in it. The pair of tunneling orbitals, which is different from the usual HOMO's of the donor and acceptor complexes, is found in a self-consistent way in a special orthogonalization procedure. This picture results in much simplified formulas for current density and for interatomic currents, as well as for the tunneling matrix element, and provides a simplified way of thinking about electron tunneling in many-electron systems. [ABSTRACT FROM AUTHOR]

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within the Kohn–Sham density functional theory for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of the warm dense matter. Generated by laser-induced compression and heating in the laboratory, the warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing with the exact quantum Monte Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used, compared with the previously reported results for the PBE, PBEsol, local-density approximation, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy. [ABSTRACT FROM AUTHOR]

The electric g-tensor is a central quantity for the interpretation of electron paramagnetic resonance spectra. In this paper, a detailed derivation of the 1-electron contributions to the g-tensor is presented in the framework of linear response theory and the second-order Douglas-Kroll-Hess (DKH) transformation. Importantly, the DKH transformation in the presence of a magnetic field is not unique. Whether or not the magnetic field is included in the required Foldy-Wouthuysen transformation, different transformation matrices and, consequently, Hamiltonians result. In this paper, a detailed comparison of both approaches is presented, paying particular attention to the mathematical properties of the resulting Hamiltonians. In contrast to previous studies that address the g-tensor in the framework of DKH theory, the resulting terms are compared to those of the conventional Pauli theory and are given a physical interpretation. Based on these mathematical and physical arguments, we establish that the proper DKH transformation for systems with constant magnetic fields is based on a gauge-invariant Foldy-Wouthuysen transformation, i.e., a Foldy-Wouthuysen transformation including the magnetic field. Calculations using density functional theory (DFT) are carried out on a set of heavy, diatomic molecules, and a set of transition-metal complexes. Based on these calculations, the performance of the relativistic calculation with and without inclusion of picture-change effects is compared. Additionally, the g-tensor is calculated for the Lanthanide dihydrides. Together with the results from the other two molecular test sets, these calculations serve to quantify the magnitude of picture-change effects and elucidate trends across the periodic table. [ABSTRACT FROM AUTHOR]

In this paper, we examine the limits of accuracy of the single determinant approximations (Hartree-Fock, optimized effective potential, and density functional theory) to the exact energy eigenstates of many electron systems. We show that an approximate Slater determinant of Sz=M gives maximum accuracy for states with S=M, provided that perturbation theory for the spin up minus spin down potential is applicable. The overlap with the exact energy eigenstates with S≠M is much smaller. Therefore, for the case that the emphasis is on wave functions, one must use symmetry preserving theories, although this is at the expense of accuracy in energy. [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]

The electronic structure and properties of PuO2 and Pu2O3 have been studied from first principles by the all-electron projector-augmented-wave method. The local density approximation+U and the generalized gradient approximation+U formalisms have been used to account for the strong on-site Coulomb repulsion among the localized Pu 5f electrons. We discuss how the properties of PuO2 and Pu2O3 are affected by the choice of U as well as the choice of exchange-correlation potential. Also, oxidation reaction of Pu2O3, leading to formation of PuO2, and its dependence on U and exchange-correlation potential have been studied. Our results show that by choosing an appropriate U, it is promising to correctly and consistently describe structural, electronic, and thermodynamic properties of PuO2 and Pu2O3, which enable the modeling of redox process involving Pu-based materials possible. [ABSTRACT FROM AUTHOR]

We propose a direct method for reducing the dimension of the space of orbital products that occur, for example, in the calculation of time dependent density functional theory linear response and in Hedin’s GW approximation to the electron propagator. We do this by defining, within the linear space of orbital products, a subspace of dominant directions that are associated with a certain eigenvalue problem. These directions span the entire linear space of products with an error that decreases approximately exponentially with their number. Our procedure works best for atomic orbitals of finite range and it avoids the use of extra sets of auxiliary fit functions. [ABSTRACT FROM AUTHOR]

A derivation of the density-functional-theory- (DFT) based reactivity indices in the ensemble unrestricted Hartree-Fock (eUHF) method is presented. The comparison between the properties of the reactivity indices evaluated in one and two sets of spin-orbital approach of the eUHF and hyper-unrestricted Hartree-Fock (UHF) methods are shown. All approaches give similar Fukui function irrespective of methodology used, but significantly differ for the global indices, containing important chemical information, and so their interpretation in terms of DFT- based indices can be questionable. The calculation scheme for the indices using the first- and second-order coupled perturbed eHF equations is proposed. A method for the identification of the spinorbitals involved in the change of the total number of electrons is included. The illustrative examples (water and hydrogen cyanide) show that the ground-state (GS) properties of the (Z±1)-electron systems can be predicted from the GS properties of the Z-electron systems with an accuracy comparable with the UHF calculations. The relaxation effect, important for the HCN system in which a change in the symmetry of the highest-occupied spin-orbital occurs, is effectively predicted. [ABSTRACT FROM AUTHOR]

This paper is an extension of our previous work on density functional models of electrons in magnetic fields. A full ‘‘classical path’’ (CP) one-body Green’s function is used in the calculation of the kinetic functional and the one particle density. This treatment leads to a more precise expression of the density functional theory in the strong B case, in which magnetic fields are much stronger than the external scalar potential. In the semiclassical limit t→0, the CP Green’s function is checked by an exact solvable system, interactionless electrons in a central harmonic potential and a constant magnetic field. It turns out that the Green’s function is correct through the order O(t2). Furthermore, in the high B limit (but still t→0), the leading terms in B of the CP Green’s function are the same as those of the exact Green’s function in the entire t-expansion series. [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]

Though contrary to conventional wisdom, the interpretation of all occupied Kohn-Sham eigenvalues as vertical ionization potentials is justified by several formal and numerical arguments. Similarly, the performance of density functional approximations (DFAs) for fractionally charged systems has been extensively studied as a measure of one- and many-electron self-interaction errors (MSIEs). These complementary perspectives (initially recognized in ab initio dft) are shown to lead to the unifying concept that satisfying Bartlett's IP theorem in DFA's mitigates self-interaction errors. In this contribution, we show that the IP-optimized QTP functionals (reparameterization of CAMB3LYP where all eigenvalues are approximately equal to vertical IPs) display reduced self-interaction errors in a variety of tests including the He2 + potential curve. Conversely, the MSIE-optimized rCAM-B3LYP functional also displays accurate orbital eigenvalues. It is shown that the CAM-QTP and rCAM-B3LYP functionals show improved dissociation limits, fundamental gaps and thermochemical accuracy compared to their parent functional CAM-B3LYP. [ABSTRACT FROM AUTHOR]

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchangecorrelation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound. [ABSTRACT FROM AUTHOR]

A local density fitting scheme is considered in which atomic orbital (AO) products are approximated using only auxiliary AOs located on one of the nuclei in that product. The possibility of variational collapse to an unphysical "attractive electron" state that can affect such density fitting [P. Merlot, T. Kjærgaard, T. Helgaker, R. Lindh, F. Aquilante, S. Reine, and T. B. Pedersen, J. Comput. Chem. 34, 1486 (2013)] is alleviated by including atom-wise semidiagonal integrals exactly. Our approach leads to a significant decrease in the computational cost of density fitting for Hartree-Fock theory while still producing results with errors 2-5 times smaller than standard, nonlocal density fitting. Our method allows for large Hartree-Fock and density functional theory computations with exact exchange to be carried out efficiently on large molecules, which we demonstrate by benchmarking our method on 200 of the most widely used prescription drug molecules. Our new fitting scheme leads to smooth and artifact-free potential energy surfaces and the possibility of relatively simple analytic gradients. [ABSTRACT FROM AUTHOR]

Using first-principles density-functional calculations, we explore the possibility of magnetic order at the rebonded DB step of the Si(001) surface. The rebonded DB step containing threefold coordinated Si atoms can be treated as a one-dimensional dangling-bond (DB) wire along the step edge. We find that Si atoms composing the step edge are displaced up and down alternatively due to Jahn-Teller-like distortion, but, if Si dimers on the terrace are passivated by H atoms, the antiferromagnetic (AFM) order can be stabilized at the step edge with a suppression of Jahn-Teller-like distortion. We also find that the energy preference of AFM order over Jahn-Teller-like distortion is enhanced in an oscillatory way as the length of DB wires decreases, showing the so-called quantum size effects. [ABSTRACT FROM AUTHOR]

We introduce a compact finite-temperature density functional model to study electron self-trapping in both liquid and vapor 3He and 4He. This model can quantitatively reproduce the most essential thermodynamic properties of 3He and 4He along their liquid-vapor coexistence lines. The structures and energetics of self-trapped electron bubbles on the 1S ground state and 1P excited state are particularly investigated. Our results show that 1S and 1P bubbles exist in liquid at any temperature, whereas 1S bubbles exist in vapor only above 1.6 K in 3He and above 2.8 K in 4He, 1P bubbles exist in vapor only above 2.5 K in 3He and 4.0 K in 4He. An initially spherical 1P bubble is unstable against deformation towards a peanut shape. In liquid, a peanut-shaped 1P bubble is held from fission by surface tension until reaching the liquid-vapor critical point, whereas in vapor it always splits into two smaller bubbles. The existence of 1P bubbles in finite-temperature liquid helium and their fission instability in helium vapor reveal interesting physics in this system. [ABSTRACT FROM AUTHOR]

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H2 and N2, and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are 'challenging problems' for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets. [ABSTRACT FROM AUTHOR]

Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such concepts are usually expressed in terms of functional derivatives with respect to the electron density, or partial derivatives with respect to the number of electrons, complicating the connection to the computational variables of the Kohn-Sham one-electron orbitals. Only recently, the analytical expressions for the chemical potential, one of the key concepts, have been derived by Cohen, Mori-Sánchez, and Yang, based on the potential functional theory formalism. In the present work, we obtain the analytical expressions for the real-space linear response function using the coupled perturbed Kohn-Sham and generalized Kohn-Sham equations, and the Fukui functions using the previous analytical expressions for chemical potentials of Cohen, Mori-Sánchez, and Yang. The analytical expressions are exact within the given exchange-correlation functional. They are applicable to all commonly used approximate functionals, such as local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals. The analytical expressions obtained here for Fukui function and linear response functions, along with that for the chemical potential by Cohen, Mori-Sánchez, and Yang, provide the rigorous and efficient evaluation of the key quantities in conceptual density functional theory within the computational framework of the Kohn-Sham and generalized Kohn-Sham approaches. Furthermore, the obtained analytical expressions for Fukui functions, in conjunction with the linearity condition of the ground state energy as a function of the fractional charges, also lead to new local conditions on the exact functionals, expressed in terms of the second-order functional derivatives. We implemented the expressions and demonstrate the efficacy with some atomic and molecular calculations, highlighting the importance of relaxation effects. [ABSTRACT FROM AUTHOR]

Iron-pyrene cluster anions, [Fem(pyrene)n]- (m = 1-2, n = 1-2) were studied in the gas phase by photoelectron spectroscopy, resulting in the determination of their electron affinity and vertical detachment energy values. Density functional theory calculations were also conducted, providing the structures and spin multiplicities of the neutral clusters and their anions as well as their respective electron affinity and vertical detachment energy values. The calculated magnetic moments of neutral Fe1(pyrene)1 and Fe2(pyrene)1 clusters suggest that a single pyrene molecule could be a suitable template on which to deposit small iron clusters, and that these in turn might form the basis of an iron cluster-based magnetic material. A comparison of the structures and corresponding photoelectron spectra for the iron-benzene, iron-pyrene, and iron-coronene cluster systems revealed that pyrene behaves more similarly to coronene than to benzene. [ABSTRACT FROM AUTHOR]

We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers. [ABSTRACT FROM AUTHOR]

We develop a new density-functional approach combining physical insight from chemical structure with treatment of multi-reference character by real-space modeling of the exchange-correlation hole. We are able to recover, for the first time, correct fractional-charge and fractional-spin behaviour for atoms of groups 1 and 2. Based on Becke's non-dynamical correlation functional [A. D. Becke, J. Chem. Phys. 119, 2972 (2003)] and explicitly accounting for core-valence separation and pairing effects, this method is able to accurately describe dissociation and strong correlation in s-shell many-electron systems. [ABSTRACT FROM AUTHOR]

The C-Hal (Hal = Cl, Br, or I) bond-length change and the corresponding vibrational frequency shift of the C-Hal stretch upon the C-Hal ...Y (Y is the electron donor) halogen bond formation have been determined by using density functional theory computations. Plots of the C-Hal bond-length change versus the corresponding vibrational frequency shift of the C-Hal stretch all give straight lines. The coefficients of determination range from 0.94366 to 0.99219, showing that the correlation between the C-Hal bond-length change and the corresponding frequency shift is very good in the halogen-bonded complexes. The possible effects of vibrational coupling, computational method, and anharmonicity on the bond-length change-frequency shift correlation are discussed in detail. [ABSTRACT FROM AUTHOR]

Dissociative electron attachment to dialanine and alanine anhydride has been studied in the gas phase utilizing a double focusing two sector field mass spectrometer. We show that low-energy electrons (i.e., electrons with kinetic energies from near zero up to 13 eV) attach to these molecules and subsequently dissociate to form a number of anionic fragments. Anion efficiency curves are recorded for the most abundant anions by measuring the ion yield as a function of the incident electron energy. The present experiments show that as for single amino acids (M), e.g., glycine, alanine, valine, and proline, the dehydrogenated closed shell anion (M-H)- is the most dominant reaction product. The interpretation of the experiments is aided by quantum chemical calculations based on density functional theory, by which the electrostatic potential and molecular orbitals are calculated and the initial electron attachment process prior to dissociation is investigated. [ABSTRACT FROM AUTHOR]

We present a systematic study on the excited electron-bubble states in superfluid 4He using a time-dependent density functional approach. For the evolution of the 1P bubble state, two different functionals accompanied with two different time-development schemes are used, namely an accurate finite-range functional for helium with an adiabatic approximation for electron versus an efficient zero-range functional for helium with a real-time evolution for electron. We make a detailed comparison between the quantitative results obtained from the two methods, which allow us to employ with confidence the optimal method for suitable problems. Based on this knowledge, we use the finite-range functional to calculate the time-resolved absorption spectrum of the 1P bubble, which in principle can be experimentally determined, and we use the zero-range functional to real-time evolve the 2P bubble for several hundreds of picoseconds, which is theoretically interesting due to the break down of adiabaticity for this state. Our results discard the physical realization of relaxed, metastable configurations above the 1P state. [ABSTRACT FROM AUTHOR]

By extrapolating the energies of nonrelativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row of the periodic table, even as Z → ∞. The local density approximation for the exchange contribution becomes more accurate (or even exact) in this limit. Extended Thomas-Fermi theory matches the shell average of both the ionization potential and density change. [ABSTRACT FROM AUTHOR]

The adiabatic approximation is problematic in time-dependent density matrix functional theory. With pure density matrix functionals (invariant under phase change of the natural orbitals) it leads to lack of response in the occupation numbers, hence wrong frequency dependent responses, in particular α(ω→0)≠α0 (the static polarizability). We propose to relinquish the requirement that the functional must be a pure one-body reduced density matrix (1RDM) functional, and to introduce additional variables which can be interpreted as phases of the one-particle states of the independent particle reference system formed with the natural orbitals, thus obtaining so-called phase-including natural orbital (PINO) functionals. We also stress the importance of the correct choice of the complex conjugation in the two-electron integrals in the commonly used functionals (they should not be of exchange type). We demonstrate with the Löwdin-Shull energy expression for two-electron systems, which is an example of a PINO functional, that for two-electron systems exact responses (polarizabilities, excitation energies) are obtained, while writing this energy expression in the usual way as a 1RDM functional yields erroneous responses. [ABSTRACT FROM AUTHOR]

We analyze the ability of spin-flip time dependent density functional theory (TD-DFT) to uniformly describe excited states of single, double, and mixed excitation character in closed-shell molecular systems, using the polyene oligomers as a primary test case. The results of comparison between conventional and spin-flip TD-DFT and with correlated ab initio methods indicate that spin-flip TD-DFT provides a more consistent description of the ordering and relative positions of the excited states than conventional TD-DFT provided a suitable exchange-correlation functional is used in the calculations. It is found that spin-flip TD-DFT provides a physically appealing picture of excitation processes which involve one or two electrons, as it captures their most important features and facilitates a more uniform description of excited states with different character. This makes spin-flip TD-DFT a promising approach for general modeling of excited states and spectra of medium and large size molecules, which exhibit low-lying excited states with strong double excitation character. [ABSTRACT FROM AUTHOR]

Parity violation (PV) effects to the electronic ground state structure for a series of chiral tungsten molecules of the type NWXYZ (X, Y, Z=H, F, Cl, Br, or I) are compared using four- (Dirac) and two- (X2C) component relativistic Hartree–Fock and density functional theories. The results show the computationally more affordable two-component X2C approach yields accurate results for all molecules investigated. The PV energy differences between the two enantiomers range from as little as 0.4 Hz for NWClBrI to 140 Hz for NWHClI using a generalized gradient approximation including exact exchange (B3LYP). The W[Single_Bond]N stretching mode in these molecules lies in the experimentally favorable CO2 laser frequency range, and we therefore investigated PV effects in vibrational transitions using a single normal mode analysis. Here the PV frequency shift between the two enantiomers ranges from 1.6 mHz for NWFBrI to 710 mHz for NWHClI. Thus these types of molecules could be useful for the future detection of PV effects in chiral molecules. [ABSTRACT FROM AUTHOR]

The Coulomb hole does not have its largest depth around an electron in or near the bond midplane. It splits into two parts, localized on both nuclear sites forming the bond. Even counterintuitive positive values of the “hole” around such a position may be observed. This happens when the Fermi hole is deeper than the total exchange-correlation hole at the reference electron position. This Coulomb “heap” is shown to arise from correlation effects on the one-electron density rather than correlation effects in the pair density. Left-right correlation tends to enhance the effect of the nuclear attraction, contracting the electron density around the nuclear positions and depleting the bond center region. Possible alternative definitions of the Coulomb hole are discussed, including one based on the exact Kohn–Sham exchange hole. Approximate density functional theory methods (generalized gradient approximation) are not accurate enough to realize the advantages of this definition. [ABSTRACT FROM AUTHOR]

A treatment of the validity of Koopmans’s theorem (KT) in the restricted open-shell Hartree–Fock (ROHF) method can be separated into two essentially different cases. The first of them involves the one-electron processes X→Xj± in which the spin state of an ion Xj± having a hole or an extra electron in the closed, open or virtual orbital [lowercase_phi_synonym]j is correctly described by a one-determinant wave function. This case was analyzed using different methods by Plakhutin et al. [J. Chem. Phys. 125, 204110 (2006)] and by Plakhutin and Davidson [J. Phys. Chem. A 113, 12386 (2009)]. In the present work we analyze more complex processes where the state of an ion cannot be described by a single determinant. An example of such processes is the removal of an alpha electron from the closed shell of a high-spin half-filled open-shell system X. For this case we give a slightly generalized formulation of KT in both the “frozen” orbital approximation (i.e., within the canonical ROHF method) and the limited configuration interaction approach for ionized systems. We also show that a simultaneous treatment of KT for all one-electron ionization processes possible leads to the necessity of introducing in the canonical ROHF method two different sets of orbitals and two respective sets of orbital energies. The theory developed is compared with the previous formulations of KT in the restricted (ROHF) and unrestricted Hartree-Fock methods, and in the unrestricted density functional theory. The practical applicability of the theory is verified by comparing the KT estimates of the vertical ionization potentials in molecules O2 and NO2 with the respective experimental data. [ABSTRACT FROM AUTHOR]

Electronic charge transfer plays an important role in novel nanostructured photovoltaic materials. Standard density functional theory (DFT) as well as time-dependent DFT severely underestimate the excitation energies related to such transitions. For the paradigmatic case of a donor-acceptor dyad formed by a zinc-porphyrin donor and a C70 fullerene acceptor these shortcomings are illustrated. A better quantitative estimate of the charge transfer energy is obtained from constrained DFT which is applied to this system in a novel implementation based on a penalty functional. [ABSTRACT FROM AUTHOR]

The Ragot–Cortona model of local correlation energy [S. Ragot and P. Cortona, J. Chem. Phys. 121, 7671 (2004)] revisits the initial approach of Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)] in order to reinstate the kinetic contribution Tc to the total correlation energy Ec. In this work, the one-electron reduced density matrix underlying the amended model is fully derived in closed form. By construction, the said density matrix is parameter-free but not N-representable, owing to approximations used in the Ragot–Cortona approach. However, the resulting density matrix is shown to have formally correct short- and long-range expansions. Furthermore, its momentum-space counterpart qualitatively agrees with known parametrized momentum distributions except at small momenta, where the disagreement reflects the nonrepresentability of the model and restricts to a small fraction of the slowest electrons only. [ABSTRACT FROM AUTHOR]

The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree–Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car–Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene. [ABSTRACT FROM AUTHOR]

We employ all-electron ab initio time-dependent density functional theory based method to calculate the long-range dipole-dipole dispersion coefficient, namely, the van der Waals (vdW) coefficient (C6) between fullerenes and finite-length carbon nanotubes as well as between these structures and different small molecules. Our aim is to accurately estimate the strength of the long-range vdW interaction in terms of the C6 coefficients between these systems and also compare these values as a function of shape and size. The dispersion coefficients are obtained via Casimir–Polder relation. The calculations are carried out with the asymptotically correct exchange-correlation potential—the statistical average of orbital potential. It is observed from our calculations that the C6 coefficients of the carbon nanotubes increase nonlinearly with length, which implies a much stronger vdW interaction between the longer carbon nanostructures compared with the shorter ones. Additionally, it is found that the values of C6 and polarizability are about 40%–50% lower for the carbon cages when compared with the results corresponding to the quasi-one-dimensional nanotubes with equivalent number of atoms. From our calculations of the vdW coefficients between the small molecules and the carbon nanostructures, it is observed that for H2, the C6 value is much larger compared with that of He. It is found that the rare gas atoms have very low values of vdW coefficient with the carbon nanostructures. In contrast, it is found that other gas molecules, including the ones that are environmentally important, possess much higher C6 values. Carbon tetrachloride as well as chlorine molecule show very high C6 values with themselves as well as with the carbon nanostructures. This is due to the presence of the weakly bound seven electrons in the valence state for the halogen atoms, which makes these compounds much more polarizable compared with the others. [ABSTRACT FROM AUTHOR]

An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster single-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD(T) methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange–correlation functionals is discussed in light of this comparison. [ABSTRACT FROM AUTHOR]

Modern density functional theory (DFT) calculations employ the Kohn–Sham system of noninteracting electrons as a reference, with all complications buried in the exchange-correlation energy (EXC). The adiabatic connection formula gives an exact expression for EXC. We consider DFT calculations that instead employ a reference of strictly correlated electrons. We define a “decorrelation energy” that relates this reference to the real system, and derive the corresponding adiabatic connection formula. We illustrate this theory in three situations, namely, the uniform electron gas, Hooke’s atom, and the stretched hydrogen molecule. The adiabatic connection for strictly correlated electrons provides an alternative perspective for understanding DFT and constructing approximate functionals. [ABSTRACT FROM AUTHOR]

Occupied-orbital dependent (OOD) exchange-correlation functionals hold a particularly prominent place in current developments of density functional theory. Their self-consistent implementation is complicated by the fact that their orbital-dependent parts are not explicit but only implicit functionals of electron density, and the exchange-correlation potential may not be obtained straightforwardly by taking the functional derivative with respect to the density. A two-step procedure is required, in which initially the functional derivatives with respect to the orbitals (FDOs) are obtained, which may then be transformed into local and multiplicative potentials by techniques of the optimized-effective potential. In view of the rather large variety of OOD functionals under current study, we report here general, systematic, and transparent expressions of the FDOs of a generalized OOD functional and additionally a matrix-element version in a basis set of atomic orbitals. Explicit FDOs are for the first time derived and numerically tested for one of the currently most complex examples of an OOD functional, Becke’s real-space model of nondynamical correlation (B05 functional) [J. Chem. Phys. 122, 064101 (2005)]. [ABSTRACT FROM AUTHOR]

The physical, structural, and chemical properties of bimetallic Pt12-nCun clusters, where n goes from 0 to 12, have been investigated within density functional theory. We find that the electronic and magnetic properties depend a lot on the atomic fraction of Cu atoms, mainly as the number of Cu atoms changes from even to odd. The chemical potential increases monotonically as a function of the Cu concentration, whereas other chemical properties such as electrophilicity depend on local changes and decreases monotonically, as well as the ionization potential. The hardness has an oscillatory behavior, which depends on the total number of electrons. The reactivity has been spatially analyzed by studying the highest occupied molecular orbital and lowest unoccupied molecular orbital. Charge delocalization is largely increased by the number of copper atoms, whereas for largely Pt concentrations, the charge is more atomiclike. That charge dependence gives another cluster outside view, which shows a rich spatial reactivity. The magnetic dependence of the cluster on the Cu atom concentration opens the door to potential chemistry applications on bimetallic magnetic nanostructures in the field of spintronics. [ABSTRACT FROM AUTHOR]

The geometrical and electronic structures of Wn (n=2–16) clusters are investigated within the framework of a gradient-corrected density functional theory. The close-packed configurations are preferred for small tungsten clusters up to n=16. The most energetic favorable structures of W14, W15, and W16 clusters, exhibiting similar electronic band structures, are all formed based on body centered cubic (bcc) unit. The clusters with size of n=8, 12, and 15 are found to be more stable with respect to their respective neighbors. The analyses of atomic orbit projected density of states and highest occupied molecular orbital, lowest unoccupied molecular orbital isosurfaces indicate that 5d electrons play a dominant role in the chemical activities of tungsten clusters. The clearly s-d hybridizations are primary presented in bonding W atoms of smaller clusters, as the cluster sizes increase, the 6p orbitals are gradually involved in chemical bonding. Our calculated vertical ionization potentials (VIPs) indicate that the W8 and W12 clusters correspond to the high VIPs. The vertical electron affinities are slightly underestimated in our investigation, but follow the trends of experimental data in principle. [ABSTRACT FROM AUTHOR]