Frozen Density Embedding with External Orthogonality in Delocalized Covalent Systems.

We present a comprehensive study of single-point kinetic energy density functionals (KEDFs) to be used in orbital-free density functional theory (DFT) calculations. We first propose a form of KEDFs based on a pointwise Kohn-Sham (KS) kinetic energy density (KED) and electron localization function (ELF) analysis. We find that the ELF and modified enhancement factor have a very strong and transferable correlation with the reduced density in various bulk metals. The non-self-consistent kinetic energy errors predicted by our KEDF models are decreased greatly compared to previously reported generalized gradient approximation (GGA) KEDFs. Second, we perform self-consistent calculations with various single-point KEDFs and investigate their numerical convergence behavior. We find striking numerical instabilities for previous GGA KEDFs; most of the GGA KEDFs fail to converge and show unphysical densities during the optimization. In contrast, our KEDFs demonstrate stable convergence, and their self-consistent results of various bulk properties agree reasonably well with KSDFT. A further detailed KED analysis reveals an interesting bifurcation phenomenon in defective metals and alloys, which may shed light on directions for future KEDF development.

We employed an explicit expression for the dispersion (D) energy in conjunction with Kohn-Sham (KS) density functional theory and frozen-density embedding (FDE) to calculate interaction energies between DNA base pairs and a selected set of amino acid pairs in the hydrophobic core of a small protein Rubredoxin. We use this data to assess the accuracy of an FDE-D approach for the calculation of intermolecular interactions. To better analyze the calculated interaction energies we furthermore propose a new energy decomposition scheme that is similar to the well-known KS bond formation analysis [F. M. Bickelhaupt and E. J. Baerends, Rev. Comput. Chem. 15, 1 (2000)], but differs in the electron densities used to define the bond energy. The individual subsystem electron densities of the FDE approach sum to the total electron density which makes it possible to define bond energies in terms of promotion energies and an explicit interaction energy. We show that for the systems considered only a few freeze-and-thaw cycles suffice to reach convergence in these individual bond energy components, illustrating the potential of FDE-D as an efficient method to calculate intermolecular interactions.

Ensemble density functional theory (DFT) furnishes a rigorous theoretical framework for describing the non-dynamic electron correlation arising from (near) degeneracy of several electronic configurations. Ensemble DFT naturally leads to fractional occupation numbers (FONs) for several Kohn-Sham (KS) orbitals, which thereby become variational parameters of the methodology. The currently available implementation of ensemble DFT in the form of the spin-restricted ensemble-referenced KS (REKS) method was originally designed for systems with only two fractionally occupied KS orbitals, which was sufficient to accurately describe dissociation of a single chemical bond or the singlet ground state of biradicaloid species. To extend applicability of the method to systems with several dissociating bonds or to polyradical species, more fractionally occupied orbitals must be included in the ensemble description. Here we investigate a possibility of developing the extended REKS methodology with the help of the generalized valence bond (GVB) wavefunction theory. The use of GVB enables one to derive a simple and physically transparent energy expression depending explicitly on the FONs of several KS orbitals. In this way, a version of the REKS method with four electrons in four fractionally occupied orbitals is derived and its accuracy in the calculation of various types of strongly correlated molecules is investigated. We propose a possible scheme to ameliorate the partial size-inconsistency that results from perfect spin-pairing. We conjecture that perfect pairing natural orbital (NO) functionals of reduced density matrix functional theory (RDMFT) should also display partial size-inconsistency.

Machine learning (ML) of kinetic energy functionals (KEFs), in particular kinetic energy density (KED) functionals, is a promising way to construct KEFs for orbital-free density functional theory (DFT). Neural networks and kernel methods including Gaussian process regression (GPR) have been used to learn Kohn-Sham (KS) KED from density-based descriptors derived from KS DFT calculations. The descriptors are typically expressed as functions of different powers and derivatives of the electron density. This can generate large and extremely unevenly distributed datasets, which complicates effective application of ML techniques. Very uneven data distributions require many training datapoints, can cause overfitting, and can ultimately lower the quality of an ML KED model. We show that one can produce more accurate ML models from fewer data by working with smoothed density-dependent variables and KED. Smoothing palliates the issue of very uneven data distributions and associated difficulties of sampling while retaining enough spatial structure necessary for working within the paradigm of KEDF. We use GPR as a function of smoothed terms of the fourth order gradient expansion and KS effective potential and obtain accurate and stable (with respect to different random choices of training points) kinetic energy models for Al, Mg, and Si simultaneously from as few as 2000 samples (about 0.3% of the total KS DFT data). In particular, accuracies on the order of 1% in a measure of the quality of energy-volume dependence B'=EV0-ΔV-2EV0+E(V0+ΔV)ΔV/V02 (where V0 is the equilibrium volume and ΔV is a deviation from it) are obtained simultaneously for all three materials.

Both model results and some exact relations concerning kinetic, exchange, and correlation energy density functionals will be presented. As to single-particle kinetic energy, a model of harmonic confinement, motivated by recent experimental activity on Fermion vapors, of an arbitrary number of Fermions will be used to construct exact nonlocal kinetic energy density functionals in both one and three dimensions. Then, some further exact results concerning nuclear cusp conditions for exchange only, and for exchange plus correlation, will be discussed. Finally, in Appendices, the one-shell harmonic confinement is generalized to include Coulomb repulsion in the two-electron Hookean atom and some results on the Pauli potentials for many-Fermion systems are obtained. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Most chemical processes happen at a local scale where only a subset of molecular orbitals is directly involved and only a subset of covalent bonds may be rearranged. To model such reactions, Density Functional Theory (DFT) is often inadequate, and the use of computationally more expensive correlated wavefunction (WF) methods is required for accurate results. Mixed-resolution approaches backed by quantum embedding theory have been used extensively to approach this imbalance. Based on the frozen density embedding freeze-and-thaw algorithm, we describe an approach to embed complete active space self-consistent field simulations run in the OpenMolcas code in a DFT environment calculated in CP2K without requiring any external tools. This makes it possible to study a local, active part of a chemical system in a larger and relatively static environment with a computational cost balanced between the accuracy of a WF method and the efficiency of DFT, which we test on environment-subsystem pairs. Finally, we apply the implementation to an oxygen molecule leaving an aluminum (111) surface and a ruthenium(IV) oxide (110) surface.

We consider an exactly soluble model consisting of two electrons attracted to a common center by harmonic-oscillator forces with mutual Coulomb repulsion between the electrons. The exact wave function and energy for the singlet ground state is obtained by separating the Schr\"odinger equation in center-of-mass and relative coordinates and numerically integrating the relative-coordinate eigenvalue equation. The exact Kohn-Sham (KS) orbital for the two equivalent electrons with opposite spins is constructed from the exact density, and the Kohn-Sham equation is inverted, yielding the exact exchange-correlation potential as a function of position.The exact correlation potential, as a function of position, is then obtained by subtracting the exact exchange potential from the exact exchange-correlation potential. The exact ground-state energy, exchange potential, correlation potential, KS single-particle energy eigenvalues ${\ensuremath{\epsilon}}_{\mathrm{KS}}$, exchange energy, and correlation energy are compared to the results given by density-functional theory employing the local-density approximation (LDA) plus correction terms and the exact KS orbitals for values of the harmonic-oscillator spring constant that vary over 4 orders of magnitude. We find that although total energies are accurately given by LDA plus correction terms, the values of ${\ensuremath{\epsilon}}_{\mathrm{KS}}$ are significantly in error. We show that this is mainly due to errors in the exchange potential.In addition we show analytically that in a singlet ground state of a two-electron system, the exact expectation value of the exchange potential equals the exact exchange energy, whereas the LDA expectation value of the exchange potential is only (2/3) the LDA exchange energy. Furthermore, we show that although the gradient expansion approximations for the exchange energy are significant improvements over the LDA, neither of these approximations significantly decreases the error in the LDA for the expectation value of the exchange potential. Both the correlation energy and the expectation value of the correlation potential in the LDA plus corrections are significantly in error when compared with the results of the exact calculation, the most accurate results being given by the LDA with self-interaction correction.

Vibrational spectra (FT-IR, FT-Raman), frontier molecular orbital, first hyperpolarizability, NBO analysis and thermodynamics properties of Piroxicam by HF and DFT methods

In the beginning of quantum mechanical Density-Functional Theory (DFT), there was the Thomas-Fermi (TF) model, which uses the electron density p(r) (a function of only 3 coordinates) as the only physical variable. Calculations with this model were inexpensive but yielded poor numerical results due to a lack of understanding of exchange-correlation effects and the kinetic-energy density functional. Many years later, Hohenberg and Kohn (HK) established the formal foundation for DFT; Kohn and Sham (KS) devised a practical implementation and brought DFT into mainstream calculations of electronic structure. Although the KS formulation allows exact evaluation of the KS kinetic energy (Ts [p]), the one-electron orbitals introduced by the KS scheme inevitably encumber the formulation in three ways: (i) 3N (vs. 3) degrees of freedom, (ii) orbital orthonormalization, and (iii) Brillouin-zone (k-point) sampling in condensed phases. Given the accuracy of DFT with present exchange-correlation density functionals, it is logical to conclude that the last frontier in DFT is a better representation of the kinetic energy solely in terms of the density. If this is true, KS orbitals will be completely eliminated from DFT formulation, and the density can be solved directly from the TF-HK equation. This is certainly superior to the KS scheme because all energy terms can be computed in momentum space with an effectively linear scaling, O(MlnM), where M is the integration grid size. This work reviews major ideas in the design of such optimal orbital-free kinetic-energy density functionals and their applications.

One obstacle in orbital-free density functional theory (OF-DFT) is the lack of accurate and transferable local pseudopotentials (LPSs). In this work, we build high quality LPSs by inverting Kohn-Sham (KS) equations on bulk valence electron densities to obtain an atom-centered local pseudopotential. With this approach, we build LPSs for Mg, Al, and Si, and then test them in KS DFT calculations of static bulk properties for several Mg, Al, and Si bulk structures as well as beta''-Al3Mg. Our Mg, Al, and Si LPSs produce correct ground state properties and phase orderings. These LPSs are then tested in KS-DFT calculations of surface energies for several low-index Mg and Al surfaces, point defect properties in hexagonal-close-packed (hcp) Mg, face-centered cubic (fcc) Al, and diamond Si, and stacking fault energies in fcc Al. All of these LPS results agree quantitatively with the results from nonlocal pseudopotentials with errors less than or equal to 40 meV per atom. Finally, we perform OF-DFT calculations for various Mg and Al structures, employing the Wang-Govind-Carter (WGC) nonlocal kinetic energy density functional (KEDF). The OF-DFT results generally agree well with the corresponding KS-DFT results. With our new Mg and Al LPSs and the WGC KEDF, OF-DFT now provides a practical method for accurate, large-scale first principles simulations of main group metals and their alloys.

The light harvesting complex II (LHCII), is a pigment-protein complex responsible for most of the light harvesting in plants. LHCII harvests sunlight and transfers excitation energy to the reaction centre of the photo-system, where the water oxidation process takes place. The energetics of LHCII can be modulated by means of conformational changes allowing a switch from a harvesting to a quenched state. In this state, the excitation energy is no longer transferred but converted into thermal energy to prevent photooxidation. Based on molecular dynamics simulations at the microsecond time scale, we have recently proposed that the switch between different fluorescent states can be probed by correlating shifts in the chromophore-chromophore Coulomb interactions to particular protein movements. However, these findings are based upon calculations in the ideal point dipole approximation (IDA) where the Coulomb couplings are simplified as first order dipole-dipole interactions, also assuming that the chromophore transition dipole moments lay in particular directions of space with constant moduli (FIX-IDA). In this work, we challenge this approximation using the time-dependent density functional theory (TDDFT) combined with the frozen density embedding (FDE) approach. Our aim is to establish up to which limit FIX-IDA can be applied and which chromophore types are better described under this approximation. For that purpose, we use the classical trajectories of solubilised light harvesting complex II (LHCII) we have recently reported [Liguori et al., Sci. Rep., 2015, 5, 15661] and selected three pairs of chromophores containing chlorophyll and carotenoids (Chl and Car): Chla611-Chla612, Chlb606-Chlb607 and Chla612-Lut620. Using the FDE in the Tamm-Dancoff approximation (FDEc-TDA), we show that IDA is accurate enough for predicting Chl-Chl Coulomb couplings. However, the FIX-IDA largely overestimates Chl-Car interactions mainly because the transition dipole for the Cars is not trivially oriented on the polyene chain.

Kinetic energy density functionals (KEDFs) approximate the kinetic energy of a system of electrons directly from its electron density. They are used in electronic structure methods that lack direct access to orbitals, for example, orbital-free density functional theory (OFDFT) and certain embedding schemes. In this contribution, we introduce libKEDF, an accelerated library of modern KEDF implementations that emphasizes nonlocal KEDFs. We discuss implementation details and assess the performance of the KEDF implementations for large numbers of atoms. We show that using libKEDF, a single computing node or (GPU) accelerator can provide easy computational access to mesoscale chemical and materials science phenomena using OFDFT algorithms. © 2017 Wiley Periodicals, Inc.

We have used density functional theory in an orbital-free, implementation to calculate the properties of pure fcc Al, hcp and bcc Mg, and the meta-stable alloy phase β′′ (Al3Mg). Five linear-response-based kinetic energy density functionals have been used, one of which has a density-dependent (DD) response kernel. We demonstrate that orbital-free density functional theory (OF-DFT) can produce physically accurate properties for Al–Mg alloys, if the kinetic energy density functional employed has a DD-kernel.

The formation and migration energies for various point defects, including vacancies and self-interstitials, in aluminium are systematically reinvestigated using the supercell approximation in the framework of orbital-free density functional theory. In particular, the finite-size effects and the accuracy of various kinetic energy density functionals are examined. It is demonstrated that as the supercell size increases, the finite-size errors asymptotically decrease as . Notably, the formation energies of self-interstitials converge much more slowly than that of vacancies. With carefully chosen kinetic energy density functionals, the calculated results agree quite well with the available experimental data and those obtained through Kohn–Sham density functional theory, which has an exact kinetic term.

We present an implementation of the coupled frozen-density embedding (FDEc) formalism for the calculation of ground-state and excited-state properties, linear-response properties, and transition moments with the coupled cluster with the singles and approximate doubles (CC2) model. Following the general strategy introduced by Höfener and Visscher [J. Chem. Theory Comput.12, 549-557 (2016)], we derive the working equations needed for the evaluation of these properties and describe their implementation into our open-source quantum chemistry program, Serenity. Our implementation comprises both projection-based embedding as well as embedding based on non-additive kinetic-energy functionals and the corresponding potentials. It makes use of the resolution-of-the-identity technique and features-in addition to CC2-the algebraic diagrammatic construction scheme of second order, ADC(2), as well as spin-component-scaled and scaled-opposite spin versions of CC2 and ADC(2). We demonstrate the capabilities of this FDEc framework by analyzing excitation energies, singlet and triplet excitation-energy splittings as well as oscillator strengths of excitonically coupled dimers, the excited-state/difference dipole moment of a formaldehyde⋯water system, and the optical rotatory dispersion of a microsolvated organic chromophore. In the latter case, we reconsider the case of (P)-dimethylallene· (H2O)2, for which uncoupled CC2-based frozen-density embedding fails, while FDEc-time-dependent density-functional theory showed promising results in earlier work. Here, we can confirm that the inclusion of system-environment response couplings leads to agreement with supermolecular CC2 results, highlighting the importance of inter-subsystem couplings in response-property calculations for molecular aggregates.