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Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used 'average of degenerate states approximation' for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases. [ABSTRACT FROM AUTHOR]

The Pauli kinetic energy functional and its functional derivative, termed Pauli potential, play a crucial role in the successful implementation of orbital-free density functional theory for electronic structure calculations. However, the exact forms of these two quantities are not known. Therefore, perforce, one employs the approximate forms for the Pauli functional or Pauli potential for performing orbital-free density functional calculations. In the present study, we developed a feed-forward neural network-based representation for the Pauli potential using a 1-dimensional (1-D) model system. We expanded density in terms of basis functions, and the coefficients of the expansion were used as input to a feed-forward neural network. Using the neural network-based representation of the Pauli potential, we calculated the ground-state densities of the 1-D model system by solving the Euler equation. We calculated the Pauli kinetic energy using the neural network-based Pauli potential employing the exact relation between the Pauli kinetic energy functional and the potential. The sum of the neural network-based Pauli kinetic energy and the von Weizsäcker kinetic energy resulted in an accurate estimation of the total kinetic energy. The approach presented in this paper can be employed for the calculation of Pauli potential and Pauli kinetic energy, obviating the need for a functional derivative. The present study is an important step in the advancement of application of machine learning-based techniques toward the orbital-free density functional theory-based methods. [ABSTRACT FROM AUTHOR]

Recent measurements of the third harmonic scattering responses of molecules have given a new impetus for computing molecular second hyperpolarizabilities (γ) and for deducing structure–property relationships. This paper has employed a variety of wavefunction and density functional theory methods to evaluate the second hyperpolarizability of the p-nitroaniline prototypical push-pull π-conjugated molecule, addressing also numerical aspects, such as the selection of an integration grid and the impact of the order of differentiation vs the achievable accuracy by using the Romberg quadrature. The reliability of the different methods has been assessed by comparison to reference Coupled-Cluster Singles and Doubles with perturbative treatment of the Triples results. On the one hand, among wavefunction methods, the MP2 scheme offers the best accuracy/cost ratio for computing the static γ. On the other hand, using density functional theory, γ remains a challenging property to compute because all conventional, global hybrid or range-separated hybrid, exchange–correlation functionals underestimate static γ values by at least 15%. Even tuning the range-separating parameter to minimize the delocalization errors does not enable to improve the γ values. Nevertheless, the original double-hybrid B2-PLYP functional, which benefits from 27% of PT2 correlation and 53% Hartree–Fock exchange, provides accurate estimates of static γ values. Unfortunately, the best performing exchange–correlation functionals for γ are not necessarily reliable for the first hyperpolarizability, β, and vice versa. In fact, the β of p-nitroaniline (pNA) could be predicted, with a good accuracy, with several hybrid exchange–correlation functionals (including by tuning the range-separating parameter), but these systematically underestimate γ. As for γ, the MP2 wavefunction method remains the best compromise to evaluate the first hyperpolarizability of pNA at low computational cost. [ABSTRACT FROM AUTHOR]

The research presented in the paper concerns the elastic properties of struvite. The article combines theoretical and experimental research. Experimental studies were carried out on struvite single crystals grown in sodium metasilicate gel by single diffusion. This unique method leads to obtaining crystals of sufficiently large size to conduct, for the first time, experimental measurement of elastic properties of monocrystalline struvite. Using the nanoindentation method, the Ez = 29.1 ± 0.7 GPa value of the component of Young's modulus was determined for a struvite single crystal. In addition, the elastic constants C11, C22, and C33 were determined using micro-Brillouin spectroscopy. Theoretical calculations of the abovementioned properties have been carried out by employing density functional theory methods. Scaling of the theoretical elastic constants leads to obtaining good agreement with the experimental values. Values of the Ex and Ey components of the Young's modulus, not available from the experimental nanoindentation technique, have been determined theoretically as 23 GPa and 27 GPa, respectively. Differences in the values of elastic components and Young's modulus components are related to the layered crystal structure of struvite and directional character of the hydrogen-bonding pattern. [ABSTRACT FROM AUTHOR]

In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn–Sham density functionals based on physical modeling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid density functional with the lowest GMTKN55 WTMAD2 "weighted total mean absolute deviation" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23." [ABSTRACT FROM AUTHOR]

In this paper, benchmark results are presented on the calculation of vertical electronic excitation energies using a long-range second-order polarization propagator approximation (SOPPA) description with a short-range density functional theory description based on the Perdew–Burke–Ernzerhof (PBE) functional. The excitation energies are investigated for 132 singlet states and 71 triplet states across 28 medium-sized organic molecules. The results show that overall SOPPA-srPBE always performs better than PBE and that SOPPA-srPBE performs better than SOPPA for singlet states, but slightly worse than SOPPA for triplet states when CC3 results are the reference values. [ABSTRACT FROM AUTHOR]

In a recent paper [A. D. Becke, J. Chem. Phys. 156, 214101 (2022)], we compared two Kohn–Sham density functionals based on physical modeling and theory with the best density-functional power series fits in the literature. With only a handful of physically motivated pre-factors, our functionals matched, and even slightly exceeded, the performance of the best power-series functionals on the general main group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. This begs the question: how much can their performance be improved by adding power-series terms of our own? We address this question in the present work. First, we describe a series expansion variable that we believe contains more local physics than any other variable considered to date. Then we undertake modest, one-dimensional fits to the GMTKN55 data with our theory-based functional corrected by power-series exchange and dynamical correlation terms. We settle on 12 power-series terms (plus six parent terms) and achieve the lowest GMTKN55 "WTMAD2" error yet reported, by a substantial margin, for a hybrid Kohn–Sham density functional. The new functional is called "B22plus." [ABSTRACT FROM AUTHOR]

Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations, efficient, accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk bandgaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performance of several advanced meta-GGA functionals in the computational prediction of band offsets at semiconductor heterojunctions. In particular, we investigate the performance of r2SCAN (two times revised strongly constrained and appropriately normed functional), rMGGAC (revised semilocal functional based on cuspless hydrogen model and Pauli kinetic energy density functional), mTASK (modified Aschebrock and Kümmel meta-GGA functional), and local modified Becke–Johnson exchange-correlation functionals. Our results strongly suggest that these meta-GGA functionals for supercell calculations perform quite well, especially, when compared to computationally more demanding GW calculations. We also present band offsets calculated using ionization potentials and electron affinities, as well as band alignment via the branch point energies. Overall, our study shows that the aforementioned meta-GGA functionals can be used within the density functional theory framework to estimate the band offsets in semiconductor heterostructures with predictive accuracy. [ABSTRACT FROM AUTHOR]

Model Hamiltonians with long-range interaction yield energies are corrected taking into account the universal behavior of the electron–electron interaction at a short range. Although the intention of this paper is to explore the foundations of using density functionals combined with range separation, the approximations presented can be used without them, as illustrated by a calculation on harmonium. In the regime, when the model system approaches the Coulomb system, they allow the calculation of ground states, excited states, and properties, without making use of the Hohenberg–Kohn theorem. Asymptotically, the technique is improvable and allows for error estimates that can validate the results. Some considerations for correcting the errors of finite basis sets in this spirit are also presented. Being related to the present understanding of density functional approximations, the results are comparable to those obtained with the latter, as long as these are accurate. [ABSTRACT FROM AUTHOR]

Proton-transfer (PT) between organic complexes is a common and important biochemical process. Unfortunately, PT energy barriers are difficult to accurately predict using density functional theory (DFT); in particular, using the generalized gradient approximation (GGA) tends to underestimate PT barriers. Moreover, PT typically occurs in environments where dispersion forces contribute to the cohesion of the system; thus, a suitable exchange-correlation functional should accurately describe both dispersion forces and PT barriers. This paper provides benchmark results for the PT barriers of several density functionals, including several variants of the van der Waals density functional (vdW-DF). The benchmark set comprises small organic molecules with inter- and intra-molecular PT. The results show that replacing GGA correlation with a fully non-local vdW-DF correlation increases the PT barriers, making it closer to the quantum chemical reference values. In contrast, including non-local correlations with the Vydrov-Voorhis method or dispersion-corrections at the DFT-D3 or the Tkatchenko–Scheffler level has barely any impact on the PT barriers. Hybrid functionals also increase and improve the energies, resulting in an excellent performance of hybrid versions of vdW-DF-cx and vdW-DF2-B86R. For the formic acid dimer PT system, we analyzed the GGA exchange and non-local correlation contributions. The analysis shows that the repulsive part of the non-local correlation kernel plays a key role in the PT energy barriers predicted with vdW-DF. [ABSTRACT FROM AUTHOR]

This paper continues the development of the molecular theory of vapor-phase nucleation presented in the preceding papers of this series and focuses on the rate of nucleation. The rate theory is developed within the definition of the modified liquid drop model of paper III, which although macroscopic in nature, is consistent with the molecular level definition of clusters found in papers I and II. In addition to providing the framework for a fully molecular rate theory, the present work provides insight into the mechanism of vapor phase nucleation. The key mechanistic result involves the natural occurrence of a non-ad hoc means of distinguishing density fluctuations that serve as embryos for the formation of liquid drops from those that do not serve in this capacity. In particular, two paths of cluster evolution are found, one leading toward drop formation through a valley on the free energy surface, the other leading toward the decay of clusters back to the supersaturated vapor. The rate of nucleation is taken as the limiting flux through the valley. The calculations for argon agree well with classical theory with respect to the prediction of the dependence of the rate on supersaturation, but differ in the prediction of the temperature dependence. At lower temperatures, the predicted rate is greater than that of classical theory, while at higher temperatures, the reverse is true. This phenomenon has also been observed by other authors using different theories. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid density functional valence bond method based on unpaired electron density, called λ-DFVB(U), is presented, which is a combination of the valence bond self-consistent field (VBSCF) method and Kohn–Sham density functional theory. In λ-DFVB(U), the double-counting error of electron correlation is mitigated by a linear decomposition of the electron–electron interaction using a parameter λ, which is a function of an index based on the number of effectively unpaired electrons. In addition, λ-DFVB(U) is based on the approximation that correlation functionals in KS-DFT only cover dynamic correlation and exchange functionals mimic some amount of static correlation. Furthermore, effective spin densities constructed from unpaired density are used to address the symmetry dilemma problem in λ-DFVB(U). The method is applied to test calculations of atomization energies, atomic excitation energies, and reaction barriers. It is shown that the accuracy of λ-DFVB(U) is comparable to that of CASPT2, while its computational cost is approximately the same as VBSCF. [ABSTRACT FROM AUTHOR]

In this paper we present a simulation study of water-like anomalies in core-softened system introduced in our previous papers. We investigate the anomalous regions for a system with the same functional form of the potential but with different parameters and show that the order of the region of anomalous diffusion and the region of density anomaly is inverted with increasing the width of the repulsive shoulder. [ABSTRACT FROM AUTHOR]

In a previous paper [J. L. McAfee and B. Poirier, J. Chem. Phys. 130, 064701 (2009)], using spin-polarized density functional theory (DFT), the authors reported a binding energy of 0.755 eV, for a single hydrogen atom adsorbed on a pristine (unrelaxed) (5,5) single-walled carbon nanotube (SWNT) substrate. A full three-dimensional (3D) potential energy surface (PES) for the SWNT-H system was also developed, and used in a quantum dynamics calculation to compute all rovibrational bound states, and associated equatorial and longitudinal adsorbate migration rates. A highly pronounced preference for the latter migration pathway at ambient temperatures was observed. In this work, we extend the aforementioned study to include multiple H-atom adsorbates. Extensive DFT calculations are performed, in order to ascertain the most relevant dynamical pathways. For two adsorbates, the SWNT-H-H system is found to exhibit highly site-specific binding, as well as long-range correlation and pronounced binding energy enhancement. The latter effect is even more pronounced in the full-hydrogenation limit, increasing the per-adsorbate binding energy to 2.6 eV. To study migration dynamics, a single-hole model is developed, for which the binding energy drops to 2.11 eV. A global 3D PES is developed for the hole migration model, using 40 radial × 18 cylindrical ab initio geometries, fit to a Fourier basis with radially dependent expansion coefficients (rms error 4.9 meV). As compared with the single-adsorbate case, the hole migration PES does not exhibit separate chemisorption and physisorption wells. The barrier to longitudinal migration is also found to be much lower. Quantum dynamics calculations for all rovibrational states are then performed (using a mixed spectral basis/phase-space optimized discrete variable representation), and used to compute longitudinal migration rates. Ramifications for the use of SWNTs as potential hydrogen storage materials are discussed. [ABSTRACT FROM AUTHOR]

Previous work testing density functionals for use in calculating high-spin–low-spin energy differences, ΔEHL, for iron(II) spin-crossover transitions has tended to conclude that only properly reparametrized hybrid functionals can predict ΔEHL since it seems to depend critically on a correct description of the electron pairing energy governed by the exchange term. Exceptions to this rule are the previous three papers (I, II, and III in the present series of papers) where it was found that modern generalized gradient approximations (GGAs) and meta-GGAs could do as well as hybrid functionals, if not better, for this type of problem. In the present paper, we extend these previous studies to five more molecules which are too large to treat with high-quality ab initio calculations, namely, the series [Fe(L)(‘NHS4’)], where NHS4=2.2′-bis(2-mercaptophenylthio)diethylamine dianion, and L=NH3, N2H4, PMe3, CO, and NO+. Since we know of no reliable experimental estimate of ΔEHL, we content ourselves with a comparison against the experimentally determined ground-state spin symmetry including, in so far as possible, finite-temperature effects. Together with the results of Papers I, II, and III, this paper provides a test of a large number of functionals against the high-spin/low-spin properties of a diverse set of Fe(II) compounds, making it possible to draw some particulary interesting conclusions. Trends among different classes of functionals are discussed and it is pointed out that there is at least one functional, namely, the OLYP generalized gradient approximation, which is able to give a reasonably good description of the delicate spin energetics of Fe(II) coordination compounds without resorting to hybrid functionals which require the relatively more expensive calculation of a Hartree–Fock-type exchange term. [ABSTRACT FROM AUTHOR]

The phase behavior of confined fluids is rich even for simple models of fluids and simple confining geometries. There has been a great deal of work to understand these systems, and density functional theories (DFT) of inhomogeneous fluids are often applied to determine phase diagrams quickly for these simple systems where symmetry in the physical problem reduces the computational problem to a one-dimensional calculation. More recently, there has been interest in developing DFT algorithms for treating fluids in complex confining geometries or at chemically heterogeneous surfaces where two- or three-dimensional calculations are required. In this paper we present three algorithms for the rapid and robust study of phase behavior in DFT models of inhomogeneous fluids and demonstrate their utility by analyzing capillary condensation in slit pores and ordered two-dimensional arrays of cylindrical fibers. The three algorithms are arclength continuation algorithms for tracing connected stable, metastable, and unstable branches, a phase transition tracking algorithm that allows for rapid computation of phase envelopes, and a spinodal tracking algorithm that allows one to assess the limits of metastability of a given state. In Paper II of this series, we apply these algorithms in a detailed investigation of capillary condensation in disordered porous media. [ABSTRACT FROM AUTHOR]

The stability of the ground or excited state calcium atom in an argon-doped helium droplet has been investigated using an extension of the helium density functional method to treat clusters. This work was motivated by the experimental study presented in a companion paper, hereafter called Paper I [A. Masson, M. Briant, J. M. Mestdagh, M. A. Gaveau, A. Hernando, and N. Halberstadt, J. Chem. Phys. 137, 184310 (2012)], which investigated Ca2 photodissociation in an argon-doped helium droplet and the nature of the fluorescent species. It is found that one single argon atom is sufficient to bring the calcium atom inside the droplet, for droplets of over 200 helium atoms. The absorption and emission spectra of CaArM (M = 0-7) clusters have been simulated using the recently developed density sampling method to describe the influence of the helium environment. Absorption spectra exhibit broad, double bands that are significantly blueshifted with respect to the calcium atomic line. The emission spectra are less broad and redshifted with respect to the calcium resonance line. The shifts are found to be additive only for M <= 2, because only the first two argon atoms are located in equivalent positions around the calcium p orbital. This finding gives a justification for the fit presented in the companion paper, which uses the observed shifts in the emission spectra as a function of argon pressure to deduce the shifts as a function of the number of argon atoms present in the cluster. An analysis of this fit is presented here, based on the calculated shifts. It is concluded that the emitting species following Ca2 photodissociation in an argon-doped droplet in Paper I could be Ca*ArM in a partly evaporated droplet where less than 200 helium atoms remain. [ABSTRACT FROM AUTHOR]

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]

Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (χ) and hardness (η) directly reflect the energy–density relationship via the chemical potential ∂E/∂N and we thus hypothesized that they probe universality. We studied χ and η for atoms Z = 1–36 using 50 diverse functionals covering all major classes. Very few functionals describe both χ and η well. η benefits from error cancellation, whereas χ is marred by error propagation from IP and EA; thus, almost all standard GGA and hybrid functionals display a plateau in the MAE at ∼0.2 eV–0.3 eV for η. In contrast, variable performance for χ indicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional, we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes "non-universality" and large dependency on exact exchange. Thus, we argue that performance for χ for the same systems is a hallmark of an important aspect of universality by probing ∂E/∂N. With this metric, B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD are the most "universal" among the tested functionals. B98 and B97-1 are accurate for very diverse metal–ligand bonds, supporting that a balanced description of ∂E/∂N and ∂E2/∂N2, via χ and η, is probably a first simple probe of universality. [ABSTRACT FROM AUTHOR]

Sulfurous acid (H2SO3) is an infamously elusive molecule. Although some theoretical papers have supposed possible roles for it in more complicated systems, it has yet to be experimentally observed. To aid experiment in detecting this molecule, we have examined the H2O + SO2 potential energy surface at the CCSDT(Q)/CBS//CCSD(T)-F12b/cc-pVTZ-F12b level of theory to resolve standing discrepancies in previous reports and predict the gas-phase vibrational spectrum for H2SO3. We find that sulfurous acid has two potentially detectable rotamers, separated by 1.1 kcal mol−1 ΔH0K with a torsional barrier of 1.6 kcal mol−1. The sulfonic acid isomer is only 6.9 kcal mol−1 above the lowest enthalpy sulfurous acid rotamer, but the barrier to form it is 57.2 kcal mol−1. Error in previous reports can be attributed to misidentified stationary points, the use of density functionals that perform poorly for this system, and, most importantly, the basis set sensitivity of sulfur. Using VPT2+K, we determine that the intense S=O stretch fundamental of each species is separated from other intense peaks by at least 25 cm−1, providing a target for identification by infrared spectroscopy. [ABSTRACT FROM AUTHOR]

This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner et al., J. Chem. Phys. 125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B 110, 18787 (2006).] This methodology allows one to redress systematic density functional theory (DFT) errors, rooted in DFT’s inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYP-LOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYP-LOC scheme is robust across different basis sets [6-31G*, 6-311++G(3df,3pd), cc-pVTZ, and aug-cc-pVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with B3LYP/6-311++G(3df,3pd)] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M05-2X functional. We conclude that although M05-2X produces better reaction enthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M05-2X than with B3LYP. A brief analysis of another functional, M06-2X, reveals that it is more accurate than M05-2X but its combination with LOC still cannot compete in accuracy with B3LYP-LOC. Indeed, B3LYP-LOC remains the best method of computing reaction enthalpies. [ABSTRACT FROM AUTHOR]

The optimized effective potential (OEP) equation can be used in a numerically efficient self-consistent form to solve for the density functional exchange and correlation potentials, as shown in a recent paper of Kümmel and Perdew [Phys. Rev. Lett. 90, 43004 (2003)]. The uniqueness of an iterative solution of the OEP equation has not yet been adequately addressed. In this paper, it is shown that no nonconstant multiplicative potentials that can contaminate an iterative solution of the OEP equation exist and, hence, that formally the exact exchange-correlation potential determined form of the OEP equation is unique to within a constant. [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]

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper presents a density functional study of multisite amphiphile molecules with the number of sites in the amphiphile ranging from 2 to 12. The molecular sites of the amphiphiles are fixed with either a freely jointed or rigid rod geometry. The difference between these two geometries is explored in detail. The paper studies the lamellar phase of these amphiphiles, as well as structures (such as monolayers and bilayers) against spherical hard bodies. The hard body surface can be tuned from solvophilic to neutral to solvophobic, and the phase behavior associated with these different arrangements is explored. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

For some time, there has been interest in understanding adsorption and capillary condensation in disordered porous media from a molecular perspective. It has been documented that the free energy landscape in these systems is complex with many metastable states. In this paper we explore the complexity of adsorption and capillary condensation in several simple models of disordered porous media constructed with parallel cylindrical fibers. We present nonlocal density functional theory calculations on a Lennard-Jones model fluid adsorbing in these porous materials coupled with the arclength continuation and phase transition tracking algorithms we presented in Paper I of this series. The arclength continuation algorithm allows us to trace out all the possible states between vapor-filled and liquid-filled pores. We find that capillary condensation is likely to occur in stages at high temperatures and strong wall-fluid interactions while the condensation occurs as a single transition at low temperatures and weak wall-fluid interactions. This paper also compares the extent of hysteresis on adsorption and desorption, discusses the validity of the Gibbs adsorption equation, and considers application of simple pore models in predicting the complexity of phase diagrams in disordered porous media. [ABSTRACT FROM AUTHOR]

The scope of this paper is the theoretical study of hydrogen atom interaction with the boron-doped graphite surface taken as a model for the interactions that occur in controlled thermonuclear fusion devices. This work is carried out in the framework of the density functional theory. The boron-doped graphite surfaces are modeled using a small modified C[sub 16]H[sub 10] cluster, in which one or two carbon atoms are substituted by boron. The efficiency of the C[sub 16]H[sub 10] cluster in modeling the H-graphite interaction has already been established in a previous paper [J. Chem. Phys. 116, 8124 (2002)]. In this study, we show that the boron atom: (i) is not a stable adsorption site for H, that it induces (ii) an increase in the H binding energy, (iii) an increase in the permeability to H of the boron-doped graphite layer, and (iv) a long range electronic perturbation in its graphitic environment. A good agreement is found between our results and experimental studies dealing with erosion mechanisms of boron-doped graphite exposed to incident hydrogen ions fluxes. [ABSTRACT FROM AUTHOR]

This is the second progress report on the study of the structure of the exact wave function. First, Theorem II of Paper I (H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000)) is generalized: when we divide the Hamiltonian of our system into N[sub D] (number of division) parts, we correspondingly have a set of N[sub D] equations that is equivalent to the Schro¨dinger equation in the necessary and sufficient sense. Based on this theorem, the iterative configuration interaction (ICI) method is generalized so that it gives the exact wave function with the N[sub D] number of variables in each iteration step. We call this the ICIND method. The ICIGSD (general singles and doubles) method is an important special case in which the GSD number of variables is involved. The ICI methods involving only one variable [ICION(one) or S(simplest)ICI] and only general singles (GS) number of variables (ICIGS) are also interesting. ICIGS may be related to the basis of the density functional theory. The convergence rate of the ICI calculations would be faster when N[sub D] is larger and when the quality of the initial guess function is better. We then study the structure of the ICI method by expanding its variable space. We also consider how to calculate the excited state by the ICIGSD method. One method is an ICI method aiming at only one exact excited state. The other is to use the higher solutions of the ICIGSD eigenvalues and vectors to compute approximate excited states. The latter method can be improved by extending the variable space outside of GSD. The underlying concept is similar to that of the symmetry-adapted-cluster configuration-interaction (SAC-CI) theory. A similar method of calculating the excited state is also described based on the ICIND method. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper proposes combining non-Boltzmann sampling with free energy perturbation to allow calculations of the free energy of hydration of a solute with both solute-water and water-water interactions with the nearest waters calculated by high-level quantum models. The method involves simulation of an approximate model of all interactions and uses both free energy perturbation and non-Boltzmann sampling to calculate the difference in energy between the approximate and quantum models. [ABSTRACT FROM AUTHOR]

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]

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 the quest towards coarse-grained potentials and new water models, we present an extension of the force matching technique to parameterize an all-atom force field for rigid water. The methodology presented here allows to improve the matching procedure by first optimizing the weighting exponents present in the objective function. A new gauge for unambiguously evaluating the quality of the fit has been introduced; it is based on the root mean square difference of the distributions of target properties between reference data and fitted potentials. Four rigid water models have been parameterized; the matching procedure has been used to assess the role of the ghost atom in TIP4P-like models and of electrostatic damping. In the former case, burying the negative charge inside the molecule allows to fit better the torques. In the latter, since short-range interactions are damped, a better fit of the forces is obtained. Overall, the best performing model is the one with a ghost atom and with electrostatic damping. The approach shown in this paper is of general validity and could be applied to any matching algorithm and to any level of coarse graining, also for non-rigid molecules. [ABSTRACT FROM AUTHOR]

Anharmonic OH phonon dispersion curves have been calculated for the Mg(OH)2 crystal. A crystal Hamiltonian was set up for the vibrational problem, where the coordinates consists of the bond lengths of two hydroxide ions in the central unit cell. Its two-dimensional potential energy surface was constructed from first principle calculations within the density functional theory approximation. Dispersion curves were calculated by diagonalizing the Hamiltonian in a basis of singly excited crystal functions. The single particle functions used to construct the crystal states were taken from a Morse oscillator basis set. These well chosen functions made it possible to restrict calculations to include only very few functions, which greatly contributed to a transparent presentation of the underlying theory. All calculations could be done analytically except for the calculation of a few integrals. We have compared our results with those of a series of harmonic lattice dynamics calculations and have found that the anharmonicity shifts the IR and Raman dispersion curves downward appreciably and slightly changes the energy differences between both curves. From an analysis of the harmonic results we conclude that incorporating the coupling between OH stretching motion and the motion of their centers of mass will appreciably change the overall features of the dispersion curves. Extension of the anharmonic model along these lines will cause no problem to the theoretical approach presented in this paper. [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]

In this paper we employ all-electron ab initio time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) C6 of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation [Phys. Rev. 3, 360 (1948)]. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation [Can. J. Phys. 58, 1200 (1980)] of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C6 and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient, and find that to a very high degree of correlation C6 scales as the square of the volume. We also present the results for van der Waals coefficient corresponding to cluster–Ar atom and cluster–N2 molecule interactions. [ABSTRACT FROM AUTHOR]

In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT), electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns (i) the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, (ii) the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and (iii) in the mapping to a model system in an excited state, the nonuniqueness of the model system wave function. According to nondegenerate ground state HKS-DFT, there exists only one local effective potential energy function, obtained as the functional derivative of the unique ground state energy functional, that can generate the ground state density. Since the theorems of ground state HKS-DFT cannot be generalized to nondegenerate excited states, there could exist different local potential energy functions that generate the excited state density. The constrained-search version of HKS-DFT selects one of these functions as the functional derivative of a bidensity energy functional. In this paper, the authors show via Q-DFT that there exist an infinite number of local potential energy functions that can generate both the nondegenerate ground and excited state densities of an interacting system. This is accomplished by constructing model systems in configurations different from those of the interacting system. Further, they prove that the difference between the various potential energy functions lies solely in their correlation-kinetic contributions. The component of these functions due to the Pauli exclusion principle and Coulomb repulsion remains the same. The existence of the different potential energy functions as viewed from the perspective of Q-DFT reaffirms that there can be no equivalent to the ground state HKS-DFT theorems for excited states. Additionally, the lack of such theorems for excited states is attributable to correlation-kinetic effects. Finally, they show that in the mapping to a model system in an excited state, there is a nonuniqueness of the model system wave function. Different wave functions lead to the same density, each thereby satisfying the sole requirement of reproducing the interacting system density. Examples of the nonuniqueness of the potential energy functions for the mapping from both ground and excited states and the nonuniqueness of the wave function are provided for the exactly solvable Hooke’s atom. The work of others is also discussed. [ABSTRACT FROM AUTHOR]

Highly precise ground state geometries, harmonic vibrational frequencies and force constants of alkaline-earth dihydrides from CaH2 to RaH2 are obtained using relativistic small-core energy-consistent effective core potentials at the coupled-cluster level. The results are compared with all-electron as well as density functional calculations. All-electron results, in particular, clearly show the importance of relativistic effects in the properties considered in this paper. The monotonic trends in the geometries are explained in terms of second-order perturbation theory. Trends in the force constants are monotonic except for the bending mode where an anomaly occurs from BaH2 to RaH2. It is rationalized in terms of reduced s-d hybridization due to relativity, which is shown to be an energy effect attributed to the stabilization of the s orbital. The pseudopotentials show an excellent performance in comparison with all-electron methods and are therefore successfully transferred to molecular cases. The density functional methods, however, suffer from functional dependencies with B3LYP performing the best in this case. [ABSTRACT FROM AUTHOR]

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2–106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT. [ABSTRACT FROM AUTHOR]

In three recent publications it was predicted that an Al4C molecule is planar on the basis of nonhybrid density functional calculations. These conclusions contradict our earlier predictions that Al4C is tetrahedral. In order to resolve the controversy we probed in this paper a potential energy surface of Al4C using a large variety of theoretical methods including multiconfigurational methods and a variety of one-electron basis sets. We confirmed that the nonhybrid Becke’s exchange with Perdew–Wang 1991 correlation functional density functional method predicts that Al4C has a planar structure in agreement with the reports of the other three groups. However, in this paper we have shown that high level ab initio calculations at the coupled cluster with singles, doubles, and noniterative triples and at the complete active space self-consistent field followed by multireference configurational interaction levels of theory confirm our earlier prediction that Al4C is indeed tetrahedral. The failure of nonhybrid density functional methods to correctly characterize the global minimum structure of Al4C demonstrates that it is dangerous to rely solely on these density functional methods in characterization of new molecules and clusters, where experimental structure is not known. [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]

Hybrid molecular dynamics (MD) simulations, which combine density functional theory (DFT) descriptions of a molecule with a molecular mechanics (MM) modeling of its solvent environment, have opened the way towards accurate computations of solvation effects in the vibrational spectra of molecules. Recently, Wheeler et al. [ChemPhysChem 4, 382 (2002)] have suggested to compute these spectra from DFT/MM-MD trajectories by diagonalizing the covariance matrix of atomic fluctuations. This so-called principal mode analysis (PMA) allegedly can replace the well-established approaches, which are based on Fourier transform methods or on conventional normal mode analyses. By scrutinizing and revising the PMA approach we identify five conditions, which must be guaranteed if PMA is supposed to render exact vibrational frequencies. Besides specific choices of (a) coordinates and (b) coordinate systems, these conditions cover (c) a harmonic intramolecular potential, (d) a complete thermal equilibrium within the molecule, and (e) a molecular Hamiltonian independent of time. However, the PMA conditions [(c)–(d)] and [(c)–(e)] are generally violated in gas phase DFT-MD and liquid phase DFT/MM-MD trajectories, respectively. Based on a series of simple analytical model calculations and on the analysis of MD trajectories calculated for the formaldehyde molecule in the gas phase (DFT) and in liquid water (DFT/MM) we show that in both phases the violation of condition (d) can cause huge errors in PMA frequency computations, whereas the inevitable violations of conditions (c) and (e), the latter being generic to the liquid phase, imply systematic and sizable underestimates of the vibrational frequencies by PMA. We demonstrate that the huge errors, which are caused by an incomplete thermal equilibrium violating (d), can be avoided if one introduces mode-specific temperatures Tj and calculates the frequencies from a “generalized virial” (GV) expression instead from PMA. Concerning ways to additionally remove the remaining errors, which GV still shares with PMA, we refer to Paper II of this work [M. Schmitz and P. Tavan, J. Chem. Phys. 121, 12247 (2004)]. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we applied a version of the nonlocal density functional theory (NLDFT) accounting radial and longitudinal density distributions to study the adsorption and desorption of argon in finite as well as infinite cylindrical nanopores at 87.3 K. Features that have not been observed before with one-dimensional NLDFT are observed in the analysis of an inhomogeneous fluid along the axis of a finite cylindrical pore using the two-dimensional version of the NLDFT. The phase transition in pore is not strictly vapor-liquid transition as assumed and observed in the conventional version, but rather it exhibits a much elaborated feature with phase transition being complicated by the formation of solid phase. Depending on the pore size, there are more than one phase transition in the adsorption-desorption isotherm. The solid formation in finite pore has been found to be initiated by the presence of the meniscus. Details of the analysis of the extended version of NLDFT will be discussed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, using density functional theory, we show the effects of explicit intermolecular hydrogen bonds on infrared spectra of glucose–water complexes. The number of explicit water molecules ranges from four to nine, and we approximate the rest of other water molecules as a continuum medium. When eight or nine water molecules are considered explicitly, our computed spectra are in good agreement with the main features of the experimental one. However, in the cases of explicit water molecules less than eight, our computed spectra are not improved successfully. This suggests that in predicting infrared spectrum of glucose in water the effects of explicit water molecules around the glucose molecule are not negligible. We also discuss the numbers of intermolecular hydrogen bonds, spectral differences between α and β anomers, and the main features of normal modes in the 1000–1200 cm-1 region. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we study nine neutral copper clusters through the theoretical characterization of their molecular structures, binding energy, electronic properties, and reactivity descriptors. Geometry optimization and vibrational analysis were performed using density functional theory calculations with a hybrid functional combined with effective core potentials. It is shown that reactivity descriptors combined with reactivity principles like the minimum polarizability and maximum hardness are operative for characterizing and rationalizing the electronic properties of copper clusters. [ABSTRACT FROM AUTHOR]

In the present work we have carried out ab initio complete active space self-consistent field (CASSCF) and second-order perturbation theory on CASSCF wave function (CASPT2) calculations and also some density functional theory calculations with the aug-cc-pVTZ Dunning's basis set on the lowest A[sub 1], B[sub 1], A[sub 2], and B[sub 2] doublet and quartet potential energy surfaces (PES) that could be involved in the title reaction. Thus, several minima, transition states, and surface crossings have been found for the C[sub 2υ]-insertion reaction mechanism. The results agree very well with available experimental data [i.e., for NO[sub 2] (²A[sub 1]), MIN2 (²B[sub 2]), NO[sub 2] (²Π[sub u])] and with other previous ab initio calculations. Six A'/A'- and four A'/A'-type surface crossings were located and classified for these PES', whose only one (i.e., ²B[sub 2]/²A[sub 1]) has been previously reported in theoretical and experimental studies. High-energy barriers were found for the direct C[sub 2υ]-insertion mechanism (3.11 and 2.54 eV for the lowest doublet and quartet PES' at the CASPT2/aug-cc-pVTZ level, respectively), clearly showing that this competitive mechanism is much less favorable than the direct C[sub s]-abstraction or the indirect C[sub s]-insertion reaction mechanisms reported in Paper I. [ABSTRACT FROM AUTHOR]

In this paper, we present the implementation of the ‘‘conductorlike screening model’’ (COSMO) into the density functional program DMol. The electronic structure and geometry of the solute are described by a density functional method (DFT). The solute is placed into a cavity which has the shape of the solute molecule. Outside of the cavity, the solvent is represented by a homogeneous dielectric medium. The electrostatic interaction between solute and solvent is modeled through cavity surface charges induced by the solvent. The COSMO theory, based on the screening in conductors, allows for the direct determination of the surface charges within the SCF procedure using only the electrostatic potentials. This represents the major computational advantage over many of other reaction field methods. Since the DMol/COSMO energy is fully variational, accurate gradients with respect to the solute coordinates can be calculated for the first time, without any restriction on the shape of the cavity. The solvation energies and optimized molecular structures are calculated for several polar solutes. In addition, the trends in basicity of amines and the relative stabilities of molecular conformers are studied. Our results suggest that for neutral solutes, agreement between calculated and experimental solvation energies of better than about 2 kcal/mol can be achieved. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Chemical reactivity theory provides a basis for predicting the reactive proclivities of molecular or condensed systems. The frontier-orbital concepts of Fukui, as generalized by Parr and collaborators within the framework of density-functional theory, were developed further by us in a previous paper (I) [J. Chem. Phys. 101, 8988 (1994)]. Nevertheless, five aspects of the theory still require further development; the reactivities are defined as local responses to global stimuli instead of nonlocal responses to local stimuli; there are ambiguities associated with the existence of energy bands in condensed systems; the theory is static and does not properly incorporate the internal dynamics of the reacting systems; the theory focuses on responses without a corresponding definition of chemical stimuli; and no connection is made with the potential energy surface and the reaction pathway. In the present paper, we concentrate on gapless systems extended in at least one dimension, metals, semimetals, and insulators. We show that taking as measures of chemical reactivity the reactivity kernels of Nalewajski [J. Chem. Phys. 78, 6112 (1983); 81, 2088 (1984); 89, 2831 (1985)] and of Berkowitz and Parr [J. Chem. Phys. 88, 2554 (1988)] in the form introduced by the latter meets the first two requirements. We find an explicit expression for the softness kernel which is a natural generalization of that found for the local softness in I.The response functions entering it are calculable via the Kohn–Sham formalism. As recognized by Nalewajski and Koninski [Z. Naturforsch. 42a, 451 (1987)], there is an infinite set of modes of chemical reactivity with corresponding spectra of softness and hardness eigenvalues. The softness spectrum has an upper bound corresponding to the most reactive mode or set of degenerate modes [Z. Naturforsh. 42a, 451 (1987)] and a vanishing lower bound. The softness kernel itself can be expressed simply in terms of the static dielectric function.... [ABSTRACT FROM AUTHOR]

Because nearest-neighbor probability distributions have been found to be useful for an exact investigation of the statistical thermodynamics of classical fluids, their exact form (valid for fluids in which many-body interaction potentials may obtain) has therefore been developed in the present paper. For an introductory familiarization with nearest-neighbor probability density functions (NNPDF’s) their connection with the commonly employed n-body distribution functions is first given. The usefulness of NNPDF’s in the analysis of structure in classical systems is also briefly discussed. A notable development associated with the paper is the fact that while ‘‘useful’’ exact expressions are not easily determined directly for n-body distribution functions (as evidenced by the several unsuccessful attempts to derive them in the literature), they are readily obtained directly for NNPDF’s (which are closely related functions) even where the ‘‘most general’’ interparticle interaction potentials may be said to obtain. [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]