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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]

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 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 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]

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]

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]

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]

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]

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 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]

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]

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]

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 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]

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]

The accurate first principles description of the correlations between electrons has been a topic of interest in molecular physics. We have reported in our previous paper [J. Chem. Phys. 123, 144112 (2005)] that the T matrix, which is the ladder diagrams up to the infinite order, can accurately represent the short-range electron correlations while calculating the double ionization energy spectra of atoms and molecules. In this paper, we calculate the two-electron distribution functions of real systems (Ar, CO, CO2, and C2H2) from the eigenvalue equation associated with the Bethe-Salpeter equation for the T matrix by beginning with the local density approximation of the density functional theory and the GW approximation. We found that when the interelectron distance is very small, the Coulomb hole appears between antiparallel spin electrons due to the short-range repulsive Coulomb interaction. The resulting two-electron distribution functions clearly show the Coulomb hole. [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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Combining simulation and model theories, this paper analyses the impact of pair dynamics on the intermolecular nuclear Overhauser effect (NOE) in liquids. For the first time, we give a distance resolved NOE. When applied to the ionic liquid 1-ethyl-3-methyl-imidazolium tetrafluoroborate the NOE turns out to be of long-range nature. This behaviour translates to the experimentally measured cross- and longitudinal relaxation rates.We were able to calculate the heteronuclear NOE from simulation data, despite the high computational effort.Model theories are computationally less demanding and cover the complete frequency range of the respective spectral density function, they are usually based on a very simple pair distribution function and the solution of the diffusion equation. In order to model the simulated data sufficiently, these simplifications in structure and dynamics have to be generalised considerably. [ABSTRACT FROM AUTHOR]

Our purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydro-carbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively low-level computational methods and compare them with higher-level reference results. To this end, the interaction of three complexes between non-polar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow high-level reference calculations of the interaction energy ΔEAB. Counterpoise-corrected interaction energies ΔEAB are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A-B complexes are carried out, using the B3LYP-D, ωB97X-D, and M06-2X functionals, with six basis sets: 6-31G(d), 6-311 (2d,p), and 6-311++G(3df,3pd); aug-cc-pVDZ and aug-cc-pVTZ; N07T. (2) Then, unconstrained optimizations by Mo\ller-Plesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [EMP2/CBS] and (ii) the higher-order correlation energy effects in passing from MP2 to CCSD(T) at the aug-cc-pVTZ basis set, ΔECC-MP, a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔEAB with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [6-31G(d) and N07T], exhibiting deviation from the computational reference of less than 1 kcal mol-1. The zero-point vibrational energy corrected estimates Δ(EAB+ZPE), obtained with the three functionals and the 6-31G(d) and N07T basis sets, are compared with experimental D0 measures, when available. In particular, this comparison is finally extended to the naphthalene and coronene dimers and to three π-π associations of different PAHs (R, made by 10, 16, or 24 C atoms) and P (80 C atoms). [ABSTRACT FROM AUTHOR]

The recent proposal to determine the (exact) correlation energy based on pairing matrix fluctuations by van Aggelen et al. ['Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation,' preprint arXiv:1306.4957 (2013)] revived the interest in the simplest approximation along this path: the particle-particle random phase approximation (pp-RPA). In this paper, we present an analytical connection and numerical demonstrations of the equivalence of the correlation energy from pp-RPA and ladder-coupled-cluster doubles. These two theories reduce to identical algebraic matrix equations and correlation energy expressions. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with coupled-cluster singles and doubles is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to design density functionals with strong ties to coupled-cluster theories and to study molecular properties at the pp-RPA level relying on well established coupled cluster techniques. [ABSTRACT FROM AUTHOR]

Methanol is the future and clean fuel, and its chemistry on metal surfaces has received much attention. In this paper we explore methanol dissociation on the clean and O or OH covered PdZn(111) that mimics Pd/ZnO catalyst studied as a promising catalyst for methanol steam reforming, using density functional theory at PW91 level and slab model. Our study demonstrates that unlike the situation on Pd (111), methanol preferentially undergoes the O-H bond scission on the PdZn (111). The presence of O and OH species hinders the C-H bond dissociation, but significantly reduces the O-H bond-breaking barrier. The present results indicate that in the course of methanol steam reforming, methanol first loses the hydrogen atom of the hydroxyl group, forming methoxy. This step is greatly enhanced when there are O and/or OH species (i.e., after water dissociation happens). Analyses reveal that CH2O is formed mainly from CH3O, not from CH2OH. [ABSTRACT FROM AUTHOR]

In this paper we present a time-domain time-dependent density functional theory (TDDFT) approach to calculate frequency-dependent polarizability and hyperpolarizabilities. In this approach, the electronic degrees of freedom are propagated within the density matrix based TDDFT framework using the efficient modified midpoint and unitary transformation algorithm. We use monochromatic waves as external perturbations and apply the finite field method to extract various orders of the time-dependent dipole moment. By fitting each order of time-dependent dipole to sinusoidal waves with harmonic frequencies, one can obtain the corresponding (hyper)polarizability tensors. This approach avoids explicit Fourier transform and therefore does not require long simulation time. The method is illustrated with application to the optically active organic molecule para-nitroaniline, of which the frequency-dependent polarizability α(-ω; ω), second-harmonic generation β(-2ω; ω, ω), optical rectification β(0; -ω, ω), third-harmonic generation γ(-3ω; ω, ω, ω), and degenerate four-wave mixing γ(-ω; ω, ω, -ω) are calculated. [ABSTRACT FROM AUTHOR]

Bi2O3 is an important metal oxide in catalysis. In this paper we employed density functional theory and slab model to investigate the surface energies and structures of various α-Bi2O3 surfaces. We first studied ten different terminations along [100] direction which has both polar and nonpolar terminations due to alternating stacking of Bi layers and O layers. Our calculated surface free energies show that the stoichiometric symmetric terminations are most stable at both high and low oxygen pressures, followed by the T2O/T4O terminations at low/high oxygen pressures. In the low Miller index planes, the (010) plane is the most stable whereas the (110) plane is the least stable. Analyses reveal that relaxation may change the surface structures significantly and there is a nice linear relationship between the surface density of broken short Bi-O bonds and the surface energy before relaxation. [ABSTRACT FROM AUTHOR]

Treatment of two-electron excitations is a fundamental but computationally expensive part of ab initio calculations of many-electron correlation. In this paper we develop a low-rank spectral expansion of two-electron excitations for accelerated electronic-structure calculations. The spectral expansion differs from previous approaches by relying upon both (i) a sum of three expansions to increase the rank reduction of the tensor and (ii) a factorization of the tensor into geminal (rank-two) tensors rather than orbital (rank-one) tensors. We combine three spectral expansions from the three distinct forms of the two-electron reduced density matrix (2-RDM), (i) the two-particle 2D, (ii) the two-hole 2Q, and the (iii) particle-hole 2G matrices, to produce a single spectral expansion with significantly accelerated convergence. While the resulting expansion is applicable to any quantum-chemistry calculation with two-particle excitation amplitudes, it is employed here in the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. The low-rank parametric 2-RDM method scales quartically with the basis-set size, but like its full-rank version it can capture multi-reference correlation effects that are difficult to treat efficiently by traditional single-reference wavefunction methods. Applications are made to computing potential energy curves of HF and triplet OH+, equilibrium bond distances and frequencies, the HCN-HNC isomerization, and the energies of hydrocarbon chains. Computed 2-RDMs nearly satisfy necessary N-representability conditions. The low-rank spectral expansion has the potential to expand the applicability of the parametric 2-RDM method as well as other ab initio methods to large-scale molecular systems that are often only treatable by mean-field or density functional theories. [ABSTRACT FROM AUTHOR]

Charge transfer from photoexcited dye molecules to a semiconductor substrate forms the basis of dye sensitized solar cells (DSCs); the overall effectiveness of a DSC device is critically dependent upon the efficiency of this process due to competition with other de-excitation channels. In this paper, we experimentally derive timescales for the charge transfer process in model water splitting DSCs. We studied two organometallic dye complexes adsorbed onto a rutile TiO2(110) substrate, the dye molecules were deposited in ultra-high vacuum using electrospray deposition. DFT simulations were used to calculate the spatial distribution of orbitals relevant to the charge transfer process. The core-hole clock implementation of resonant photoemission spectroscopy was used to determine upper limits on charge transfer timescales for previously unoccupied orbitals, which were found to be in the low-femtosecond regime apart from one orbital found to have an upper limit in the sub-femtosecond regime. [ABSTRACT FROM AUTHOR]

The understanding of phase behavior of copolymer brushes is of fundamental importance for the design of smart materials. In this paper, we have performed classical density functional theory calculations to study diblock copolymer brushes (A-B) in an explicit solvent which prefers the A block to B block. With increasing B-block length (NB), we find a structural transition of the copolymer brush from mixed to collapsed, partial-exposed, and exposed structure, which is qualitatively consistent with experiments. The phase transitions are attributed to the interplay between entropic cost of folding copolymer brushes and enthalpic effect of contact between unlike components. In addition, we examine the effect of different parameters, such as grafting density (ρg), the bottom block length (NA), and the chain length of solvent (NS) on the solvent response of copolymer brushes. The transition chain length (NB) increases with decreasing ρg and NA, and a smaller solvent molecule makes the collapsed structure less stable due to its lower penetration cost. Our results provide the insight to phase behavior of copolymer brushes in selective solvents from a molecular view. [ABSTRACT FROM AUTHOR]

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

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]

The structural and energetic properties of purely siliceous, proton-, and Cu- and Co-exchanged chabazite have been studied using periodic density-functional (DFT) calculations with both conventional gradient-corrected exchange-correlation functionals and hybrid functionals mixing exact (i.e., Hartree-Fock) and DFT exchange. Spin-polarized and fixed-moment calculations have been performed to determine the equilibrium and excited spin-configurations of the metal-exchanged chabazites. For the purely siliceous chabazite, hybrid functionals predict a slightly more accurate cell volume and lattice geometry. For isolated Al/Si substitution sites, gradient-corrected functionals predict that the lattice distortion induced by the substitution preserves the local tetrahedral symmetry, whereas hybrid functionals lead to a distorted Al coordination with two short and two long Al-O bonds. Hybrid functionals yield a stronger cation-framework binding that conventional functionals in metal-exchanged zeolites, they favor shorter cation-oxygen bonds and eventually also a higher coordination of the cation. Both types of functionals predict the same spin in the ground-state. The structural optimization of the excited spin-states shows that the formation of a high-spin configuration leads to a strong lattice relaxation and a weaker cation-framework bonding. For both Cu- and Co-exchanged chabazite, the prediction of a preferred location of the cation in a six-membered ring of the zeolite agrees with experiment, but the energy differences between possible cation locations and the lattice distortion induced by the Al/Si substitution and the bonding of the cation depends quite significantly on the choice of the functional. All functionals predict similar energy differences for excited spin states. Spin-excitations are shown to be accompanied by significant changes in the cation coordination, which are more pronounced with hybrid functionals. The consequences of electronic spectra and chemical reactivity are analyzed in the following papers. [ABSTRACT FROM AUTHOR]

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

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]

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

The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations. [ABSTRACT FROM AUTHOR]

We locate the putative global minimum structures of NaxCs55 - x and LixCs55 - x nanoalloys through combined empirical potential and density functional theory calculations, and compare them to the structures of 55-atom Li-Na and Na-K nanoalloys obtained in a recent paper [A. Aguado and J. M. López, J. Chem. Phys. 133, 094302 (2010)]. Alkali nanoalloys are representative of isovalent metallic mixtures with a strong tendency towards core-shell segregation, and span a wide range of size mismatches. By comparing the four systems, we analyse how the size mismatch and composition affect the structures and relative stabilities of these mixtures, and identify useful generic trends. The Na-K system is found to possess a nearly optimal size mismatch for the formation of poly-icosahedral (pIh) structures with little strain. In systems with a larger size mismatch (Na-Cs and Li-Cs), frustration of the pIh packing induces for some compositions a reconstruction of the core, which adopts instead a decahedral packing. When the size mismatch is smaller than optimal (Li-Na), frustration leads to a partial amorphization of the structures. The excess energies are negative for all systems except for a few compositions, demonstrating that the four mixtures are reactive. Moreover, we find that Li-Cs and Li-Na mixtures are more reactive (i.e., they have more negative excess energies) than Na-K and Na-Cs mixtures, so the stability trends when comparing the different materials are exactly opposite to the trends observed in the bulk limit: the strongly non-reactive Li-alkali bulk mixtures become the most reactive ones at the nanoscale. For each material, we identify the magic composition xm which minimizes the excess energy. xm is found to increase with the size mismatch due to steric crowding effects, and for LixCs55 - x the most stable cluster has almost equiatomic composition. We advance a simple geometric packing rule that suffices to systematize all the observed trends in systems with large size mismatch (Na-K, Na-Cs, and Li-Cs). As the size mismatch is reduced, however, electron shell effects become more and more important and contribute significantly to the stability of the Li-Na system. [ABSTRACT FROM AUTHOR]