About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

Kinetic energy density for orbital‐free density functional calculations by axiomatic approach

An axiomatic approach is herein used to determine the physically acceptable forms for general D‐dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one‐point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large‐scale orbital free density functional theory calculations.     

A simple approximation for the Pauli potential yielding self‐consistent electron densities exhibiting proper atomic shell structure

A simple approximation for the Pauli potential for the groundstate of atomic systems is given, which in connection with Hohenberg–Kohn variational procedure yields self‐consistent electron densities exhibiting proper atomic shell structure. © 2015 Wiley Periodicals, Inc.     

Assessing the role of Hartree‐Fock exchange,correlation energy and long range corrections in evaluating ionization potential,and electron affinity in density functional theory

Accurate determination of ionization potentials (IPs), electron affinities (EAs), fundamental gaps (FGs), and HOMO, LUMO energy levels of organic molecules play an important role in modeling and predicting the efficiencies of organic photovoltaics, OLEDs etc. In this work, we investigate the effects of Hartree Fock (HF) Exchange, correlation energy, and long range corrections in predicting IP and EA in Hybrid Functionals. We observe increase in percentage of HF exchange results in increase of IPs and decrease in EAs. Contrary to the general expectations inclusion of both HF exchange and correlation energy (from the second order perturbation theory MP2) leads to poor prediction. Range separated Hybrid Functionals are found to be more reliable among various DFT Functionals investigated. DFT Functionals predict accurate IPs whereas post HF methods predict accurate EAs. © 2017 Wiley Periodicals, Inc.     

Compatibility of correlation‐consistent basis sets with a hybrid Hartree–Fock/density functional method

The present study examines the feasibility of combining the correlation‐consistent basis sets developed by Dunning and coworkers with the hybrid Hartree–Fock/density functional method B3LYP. Furthermore, extrapolation to the complete basis set (CBS) limit minimizes errors due to the presence of an incomplete basis set and can act as a rigorous test of the limitations of the B3LYP method. Equilibrium geometries, energies, and harmonic vibrational frequencies were determined for a series of well‐studied, yet computationally challenging, small inorganics and their respective ions. The results were then extrapolated to the CBS limit, where applicable, and compared to experiment. It was found that a union between the hybrid Hartree–Fock/density functional B3LYP method and Dunning's augmented correlation‐consistent basis sets gave results that were comparable to molecular orbital methods that explicitly account for electron correlation. Furthermore, the minimum basis set necessary to attain reasonable results for the systems studied was aug‐cc‐pVTZ. Upgrading to the aug‐cc‐pVQZ level and subsequent extrapolation to the CBS limit further improved the overall agreement with the experiment. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 207–216, 1999     

Electron correlations in Kohn–Sham exchange‐only theory

We provide an interpretation for the “exchange” energy and potential of Kohn–Sham exchange‐only theory, or equivalently that of the optimized potential method (OPM), which shows that in addition to contribution due to the Pauli exclusion principle, there is a kinetic component to these properties. The interpretation is in terms of a conservative field R ^OPM( r ), which is a sum of two fields, one representative of Pauli electron correlations and the other of kinetic effects. The OPM exchange potential is derived via the differential virial theorem to be the work done to move an electron in the field R ^OPM( r ). The OPM exchange energy is then expressed via the integral virial theorem in terms of this field. A similar interpretation for the energy and potential may also be derived directly from the OPM integral equation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71:473–480, 1999     

Interesting properties of Thomas–Fermi kinetic and Parr electron–electron‐repulsion DFT energy functional generated compact one‐electron density approximation for ground‐state electronic energy of molecular systems

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a (nonlinear, approximate) density functional of three spatial dimension one‐electron density for an N‐electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas‐Fermi kinetic energy (～∫ρ^5/3d r ₁) and Parr electron–electron repulsion energy (～∫ρ^4/3d r ₁) main‐term functionals are accepted, and they should, the later described, compact one‐electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg–Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground‐state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one‐electron density models. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Hierarchy of equations in the generalized density functional theory

Functional relations and equations of hierarchy in the generalized density functional theory (DFT) are derived from coordinate scaling and adiabatic connection. Local and nonlocal solutions for the noninteracting kinetic energy, exchange energy, correlation energy, and the kinetic energy correction functionals are presented. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Proof of finiteness of Kohn–Sham theory electron interaction potential at the nucleus of atoms

We employ Kato's theorem to prove that the electron interaction potential of Kohn–Sham density functional theory is finite at the nucleus of spherically symmetric and sphericalized atoms and ions. Therefore, this finiteness is a direct consequence of the electron–nucleus cusp condition for the density. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 205–208, 2000     

Comparative studies on the structures,infrared spectrum,and thermodynamic properties of phthalocyanine using ab initio Hartree–Fock and density functional theory methods

The molecular structure, vibrational spectrum, standard thermodynamic functions, and enthalpy of formation of free base phthalocyanine (Pc) have been studied using the density functional theory B3LYP procedure, as well as the ab initio Hartree–Fock method. Various basis sets 3‐21G, 6‐31G*, and LANL2DZ have been employed. The results obtained at various levels are discussed and compared with each other and with the available experimental data. It is shown that calculations performed at the Hartree–Fock level cannot produce a reliable geometry and related properties such as the dipole moment of Pc and similar porphyrin‐based systems. Electron correlation must be included in the calculations. The basis set has comparatively less effect on the calculated results. The results derived at the B3LYP level using the smaller 3‐21G and LANL2DZ basis sets are very close to those produced using the medium 6‐31G* basis set. The geometry of Pc obtained at the B3LYP level has D_2h symmetry and the diameter of the central macrocycle is about 4 Å. The enthalpy of formation of Pc in the gas phase has been predicted to be 1518.50 kJ/mol at the B3LYP/6‐311G(2d,2p)//B3LYP/6‐31G* level via an isodesmic reaction. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Determining the role of the underlying orbital‐dependence of PBE0‐DH and PBE‐QIDH double‐hybrid density functionals

We study the orbital‐dependence of three (parameter‐free) double‐hybrid density functionals, namely the PBE0‐DH, the PBE‐QIDH models, and the SOS1‐PBE‐QIDH spin‐opposite‐scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self‐consistent density functional theory calculations using several exchange‐correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF‐PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self‐interaction errors. We find that the PBE‐QIDH double‐hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.     

First‐order correlation‐kinetic contribution to Kohn–Sham exchange charge density function in atoms,using quantal density functional theory approach

Using the static exchange‐correlation charge density concept, the total integrated exchange‐charge density function is calculated within the nonrelativistic spin‐restricted exchange‐only (i) optimized effective potential model, and (ii) nonvariational local potential derived from the exchange‐only work potential within the quantal density functional theory, for the ground‐state isoelectronic series: Ga⁺, Zn, Cu^?; In⁺, Cd, Ag^?; and Tl⁺, Hg, Au^?. The difference between the exchange charge density function derived from these potentials is employed to evaluate the first‐order correlation‐kinetic contribution to the integrated exchange charge density. This contribution is found to be important for both the intra‐ and inter‐shell regions. Screening effects on the contribution due to the nd¹⁰ (n = 3–5) subshells are discussed through comparisons with similar calculations on Ca, Sr, and Ba, wherein nd¹⁰ electrons are absent. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Post Hartree–Fock and density functional theory studies on Di-Protonated Allopurinol

Post Hartree–Fock and density functional theory (DFT) methods have been employed to study the molecular properties of Di-Protonated Allopurinol²⁺ tautomers in gaseous and aqueous phase environments. The tautomers in gaseous phase have been optimized at MP2/6-311G(2d,2p) and B3LYP/6-311G(2d,2p) levels of theory. The self-consistent reaction field theory (SCRF) has been employed to optimize the tautomers in aqueous phase (ε = 78.5) at B3LYP/6-311G(2d,2p) level of theory and the solvent effect has been studied. The structure, energetics and relative stabilities of the tautomers have been analyzed both in gaseous and aqueous phases. The principle of maximum hardness (MHP) has been tested at B3LYP/6-311G(2d,2p) level of theory. The condensed Fukui functions have been calculated using the atomic charges obtained through Natural population analysis to identify the relative change in the most reactive site of the optimized structures. NMR studies have been carried out, on the basis of Cheeseman coworker’s method, to analyze the molecular environment as well as the delocalization activities of electron clouds.     

About the difference between density functionals defined by energy criterion and density functionals defined by density criterion: Exchange functionals

The difference between density functionals defined by energy criterion and density functionals defined by density criterion is studied for the exchange functional. It is shown that Slater potentials are exact exchange potentials in the sense that they yield the Hartree–Fock electron density if all operators are given by local expressions. © 2016 Wiley Periodicals, Inc.     

Modeling exact exchange potential in spherically confined atoms

In this work, local exchange potentials corresponding to the Hartree–Fock (HF) electron density have been obtained using the Zhao–Morrison–Parr method for a number of closed‐shell confined atoms and ions. The exchange potentials obtained and the resulting density were compared with those given by the Becke–Johnson (BJ) model potential. It is demonstrated that introducing a scaling factor to the BJ potential allows improving the quality of the resulting density. The optimum scaling factor increases with decreasing confinement radius. The performance of Karasiev and Ludeña's SCα‐LDA method as well as of the Becke‐88 exchange potential for reproducing the HF electron densities in confined atoms has been also examined. © 2015 Wiley Periodicals, Inc.     

Ab initio fragment orbital‐based theory

A new formulation of ab initio theory is presented that treats a large molecule in terms of wave functions of its constituent molecular subunits (to be called fragments). The method aims to achieve near conventional ab initio accuracy but using a truncated set of fragment orbitals with a consequent drastic reduction of computing time and storage requirement. Illustrative calculations are presented for the molecule amino‐nitro‐stilbene. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Grid‐based density functional calculations of many‐electron systems

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many‐electron systems in the 3D cartesian coordinate grid (CCG). The atom‐centered localized gaussian basis set, electronic density, and the two‐body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange‐correlation potential, while Hay‐Wadt‐type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom‐centered grid as well as the grid‐free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many‐electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.