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The development of kinetic energy (KE) functionals is one of the current challenges in density functional theory (DFT). The Yukawa non-local KE functionals [Phys. Rev. B 103, 155127 (2021)] have been shown to describe accurately the Lindhard response of the homogeneous electron gas (HEG) directly in the real space, without any step in the reciprocal space. However, the Yukawa kernel employs an exponential function which cannot be efficiently represented in conventional Gaussian-based quantum chemistry codes. Here, we present an expansion of the Yukawa kernel in Gaussian functions. We show that for the HEG this expansion is independent of the electronic density, and that for general finite systems the accuracy can be easily tuned. Finally, we present results for atomistic sodium clusters of different sizes, showing that simple Yukawa functionals can give superior accuracy as compared to semilocal functionals., Comment: 9 pages, 6 figures

Adiabatic connection models (ACMs), which interpolate between the limits of weak and strong interaction, are powerful tools to build accurate exchange-correlation functionals. If the exact weak-interaction expansion from second-order perturbation theory is included, a self-consistent implementation of these functionals is challenging and still absent in the literature. In this work we fill this gap by presenting a fully self-consistent-field (SCF) implementation of some popular ACM functionals. While using second-order perturbation theory at weak interactions, we have also introduced new generalised gradient approximations (GGA's), beyond the usual point-charge-plus-continuum model, for the first two leading terms at strong interactions, which are crucial to ensure robustness and reliability. We then assess the SCF-ACM functionals for molecular systems and for prototypical strong-correlation problems. We find that they perform well for both the total energy and the electronic density and that the impact of SCF orbitals is directly connected to the accuracy of the ACM functional form. For the H$_2$ dissociation the SCF-ACM functionals yield significant improvements with respect to standard functionals, also thanks to the use of the new GGA's for the strong-coupling functionals., Comment: 40 pages, 6 figures

We have studied the correlation potentials produced by various adiabatic connection models (ACM) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order G\"orling-Levy (GL2) potentials, and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-interaction limit potentials has also been investigated and discussed., Comment: 16 pages, 10 figures

Approximate exchange-correlation functionals built by modeling in a non-linear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameters-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than the second-order perturbation theory., Comment: 6 pages, 3 figures

Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of non-local functionals, possibly employing system dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that instead properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian-level of theory, can indeed achieve similar accuracy as non-local functionals and can be accurate for both metals and semiconductors, without the need of system-dependent parameters., Comment: 19 pages, 3 figures

Orbital-Free Density Functional Theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the approximation made for the kinetic energy (KE) functional. To date, the most accurate KE functionals are non-local functionals based on the linear-response kernel of the homogeneous electron gas, i.e. the jellium model. Here, we use the linear-response kernel of the jellium-with-gap model, to construct a simple non-local KE functional (named KGAP) which depends on the band gap energy. In the limit of vanishing energy-gap (i.e. in the case of metals), the KGAP is equivalent to the Smargiassi-Madden (SM) functional, which is accurate for metals. For a series of semiconductors (with different energy-gaps), the KGAP performs much better than SM, and results are close to the state-of-the-art functionals with complicated density-dependent kernels., Comment: 11 pages, 4 figure

The performance of functionals based on the idea of interpolating between the weak and the strong-interaction limits the global adiabatic-connection integrand is carefully studied for the challenging case of noble-metal clusters. Different interpolation formulas are considered and various features of this approach are analyzed. It is found that these functionals, when used as a correlation correction to Hartree-Fock, are quite robust for the description of atomization energies, while performing less well for ionization potentials. Future directions that can be envisaged from this study and a previous one on main group chemistry are discussed., Comment: 16 pages, 6 figures

We investigate a highly-nonlocal generalization of the Lindhard function, given by the jellium-with-gap model. We find a band-gap-dependent gradient expansion of the kinetic energy, which performs noticeably well for large atoms. Using the static linear response theory and the simplest semilocal model for the local band gap, we derive a non-empirical generalized gradient approximation (GGA) of the kinetic energy. This GGA kinetic energy functional is remarkably accurate for the description of weakly interacting molecular systems within the subsystem formulation of Density Functional Theory., Comment: 9 pages, 2 figures

The development of semilocal models for the kinetic energy density (KED) is an important topic in density functional theory (DFT). This is especially true for subsystem DFT, where these models are necessary to construct the required non-additive embedding contributions. In particular, these models can also be efficiently employed to replace the exact KED in meta-Generalized Gradient Approximation (meta-GGA) exchange-correlation functionals allowing to extend the subsystem DFT applicability to the meta-GGA level of theory. Here, we present a two-dimensional scan of semilocal KED models as linear functionals of the reduced gradient and of the reduced Laplacian, for atoms and weakly-bound molecular systems. We find that several models can perform well but in any case the Laplacian contribution is extremely important to model the local features of the KED. Indeed a simple model constructed as the sum of Thomas-Fermi KED and 1/6 of the Laplacian of the density yields the best accuracy for atoms and weakly-bound molecular systems. These KED models are tested within subsystem DFT with various meta-GGA exchange-correlation functionals for non-bonded systems, showing a good accuracy of the method., Comment: 11 pages, 5 figures

We have tested the original interaction-strength-interpolation (ISI) exchange-correlation functional for main group chemistry. The ISI functional is based on an interpolation between the weak and strong coupling limits and includes exact-exchange as well as the G\"orling-Levy second-order energy. We have analyzed in detail the basis-set dependence of the ISI functional, its dependence on the ground-state orbitals, and the influence of the size-consistency problem. We show and explain some of the expected limitations of the ISI functional (i.e. for atomization energies), but also unexpected results, such as the good performance for the interaction energy of dispersion-bonded complexes when the ISI correlation is used as a correction to Hartree-Fock., Comment: 20 pages, 20 figures

We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e. the electron density, its gradient and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for {the exchange of} any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob's ladder classification of non-empirical density functionals., Comment: 14 pages, 9 figures

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals., Comment: 11 pages, 7 figures

Using the semiclassical neutral atom theory, we extend to fourth order the modified gradient expansion of the exchange energy of density functional theory. This expansion can be applied both to large atoms and solid-state problems. Moreover, we show that it can be employed to construct a simple and non-empirical generalized gradient approximation (GGA) exchange-correlation functional competitive with state-of-the-art GGAs for solids, but also reasonably accurate for large atoms and ordinary chemistry., Comment: 10 pages, 7 figures

Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the non-locality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the image-like surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to the ones at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics., Comment: 6 pages, 4 figures

We assess the Tognetti-Cortona-Adamo (TCA) generalized gradient approximation correlation functional [J. Chem. Phys. 128:034101 (2008)] for a variety of electronic systems. We find that, even if the TCA functional is not exact for the uniform electron gas, it is very accurate for the jellium surface correlation energies and it gives a realistic description of the quantum oscillations and surface effects of various jellium clusters, that are important model systems in computational chemistry and solid-state physics. When the TCA correlation is combined with the non-empirical PBEint, Wu-Cohen, and PBEsol$_b$ exchange functionals, the resulting exchange-correlation approximations provide good performances for a broad palette of systems and properties, being reasonably accurate for thermochemistry and geometry of molecules, transition metal complexes, non-covalent interactions,equilibrium lattice constants, bulk moduli, and cohesive energies of solids., Comment: 14 pages, 6 figures

Using the observed proportionality of CCSD(T) and MP2 correlation interaction energies [I. Grabowski, E. Fabiano, F. Della Sala, Phys. Chem. Chem. Phys. 15, 15485 (2013)] we propose a simple scaling procedure to compute accurate interaction energies of non-covalent complexes. Our method makes use of MP2 and CCSD(T) correlation energies, computed in relatively small basis sets, and fitted scaling coefficients to yield interaction energies of almost complete basis set limit CCSD(T) quality. Thanks to the good transferability of the scaling coefficients involved in the calculations, good results can be easily obtained for different intermolecular distances., Comment: 8 pages, 4 figures

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes the problem and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method., Comment: 14 pages, 3 figures

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided., Comment: 12 pages, 4 figures

We show that the Kohn-Sham positive-definite kinetic energy (KE) density significantly differs from the von Weizs\"acker (VW) one at the nuclear cusp as well as in the asymptotic region. At the nuclear cusp, the VW functional is shown to be linear and the contribution of p-type orbitals to the KE density is theoretically derived and numerically demonstrated in the limit of infinite nuclear charge, as well in the semiclassical limit of neutral large atoms. In the latter case, it reaches 12 of the KE density. In the asymptotic region we find new exact constraints for meta Generalized Gradient Approximation (meta-GGA) exchange functionals: with an exchange enhancement factor proportional to $\sqrt{\alpha}$, where $\alpha$ is the common meta-GGA ingredient, both the exchange energy density and the potential are proportional to the exact ones. In addition, this describes exactly the large-gradient limit of quasi-two dimensional systems., Comment: 5 pages, 3 figures

We propose a simple gradient-dependent bound for the exchange-correlation energy (sLL), based on the recent non-local bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly-varying density cases but it is tighter for slowly-varying density systems. To show the utility of the sLL bound we apply it to the construction of simple semilocal and non-local exchange and correlation functionals. In both cases improved results, with respect to the use of Lieb-Oxford bound, are obtained showing the power of the sLL bound., Comment: 5 pages, 2 figures

The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analyzed. The relative importance of singly- and doubly- excited contributions as well as the effect of scaling the same- and opposite- spin components is investigated in detail comparing OEP results with Kohn-Sham (KS) quantities determined via an inversion procedure using accurate ab initio electronic densities. Special attention is dedicated in particular to the recently proposed scaled-opposite-spin OEP functional [I. Grabowski, E. Fabiano and F. Della Sala, Phys. Rev. B, 87, 075103, (2013)] which is the most advantageous from a computational point of view. We find that for high accuracy a careful, system dependent, selection of the scaling coefficient is required. We analyze several size-extensive approaches for this selection. Finally, we find that a composite approach, named OEP2-SOSh, based on a post-SCF rescaling of the correlation energy can yield high accuracy for many properties, being comparable with the most accurate OEP procedures previously reported in the literature but at substantially reduced computational effort., Comment: 14 pages, 4 figures

We performed a benchmark study on a series of dihydrogen bond complexes and constructed a set of reference bond distances and interaction energies. The test set was employed to assess the performance of several wave-function correlated and density functional theory methods. We found that second-order correlation methods describe relatively well the dihydrogen complexes. However, for high accuracy inclusion of triple contributions is important. On the other hand, none of the considered density functional methods can simultaneously yield accurate bond lengths and interaction energies. However, we found that improved results can be obtained by the inclusion of non-local exchange contributions., Comment: 15 pages, 7 figures

We study the uniform electron gas with a gap model in the context of density functional theory. Based on this analysis, we construct two local gap models that realize generalized gradient approximation (GGA) correlation functionals satisfying numerous exact constraints for the correlation energy. The first one, named GAPc, fulfills the full second-order correlation gradient expansion at any density regime, is very accurate for jellium surfaces, comparable to state-of-the-art GGAs for atomic systems and molecular systems, and well compatible with known semilocal exchange. The second functional, named GAPloc, is satisfying the same exact conditions, except that the second-order gradient expansion is sacrificed for a better behavior under the Thomas-Fermi scaling and a more realistic correlation energy density of the hellium atom. The GAPloc functional displays a high accuracy for atomic correlation energies, still preserving a reasonable behavior for jellium surfaces. Moreover, it shows a higher compatibility with the Hartree-Fock exchange than other semilocal correlation functionals. This feature is explained in terms of the real-space analysis of the GAPloc correlation energy., Comment: 14 pages, 4 figures

We test Laplacian-level meta-generalized gradient approximation (meta-GGA) non-interacting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We consider several well known Laplacian-level meta-GGAs from literature (bare GE4, modified GE4, and the MGGA functional of Perdew and Constantin [Phys. Rev. B \textbf{75},155109 (2007)]), as well as two newly designed Laplacian-level kinetic energy functionals (named L0.4 and L0.6). First, a general assessment of the different functionals is performed, testing them for model systems (one-electron densities, Hooke's atom and different jellium systems), atomic and molecular kinetic energies as well as for their behavior with respect to density-scaling transformations. Finally, we assess, for the first time, the performance of the different functionals for Subsystem Density Functional Theory (DFT) calculations on non-covalently interacting systems. We find that the different Laplacian-level meta-GGA kinetic functionals may improve the description of different properties of electronic systems but no clear overall advantage is found over the best GGA functionals. Concerning Subsystem DFT calculations, the here proposed L0.4 kinetic energy functional is competitive with state-of-the-art GGAs, whereas all other Laplacian-level functionals fail badly. The performance of the Laplacian-level functionals is rationalized thanks to a two-dimensional reduced-gradient and reduced-Laplacian decomposition of the non-additive kinetic energy density., Comment: 19 pages, 6 figures

We extend the frozen density embedding theory to non-integer subsystems' particles numbers. Different features of this formulation are discussed, with special concern for approximate embedding calculations. In particular, we highlight the relation between the non-integer particle-number partition scheme and the resulting embedding errors. Finally, we provide a discussion of the implications of the present theory for the derivative discontinuity issue and the calculation of chemical reactivity descriptors., Comment: 14 pages, 4 figures

We present a density difference based analysis for a range of orbital--dependent Kohn--Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio wave-function calculations. Particular attention is paid to the quality of approximations to the exchange--only optimized effective potential (OEP) approach: we consider both the Localized Hartree Fock as well as the Krieger-Li-Iafrate methods. Analysis of density differences at the exchange--only level reveals the impact the approximations have on the resulting electronic densities. These differences are further quantified in terms of the ground state energies, frontier orbital energy differences and highest occupied orbital energies obtained. At the correlated level an OEP approach based on a perturbative second--order correlation energy expression is shown to deliver results comparable with those from traditional wave function approaches, making it suitable for use as a benchmark against which to compare standard density--functional approximations., Comment: 12 pages, 3 figures

Using a reverse-engineering method we construct a meta-generalized gradient approximation (meta-GGA) angle-averaged exchange-correlation hole model which has a general applicability. It satisfies known exact hole constraints and can exactly recover the exchange-correlation energy density of any reasonable meta-GGA exchange-correlation energy functional satisfying a minimal set of exact properties. The hole model is applied to several non-empirical meta-GGA functionals: the Tao-Perdew-Staroverov-Scuseria (TPSS), the revised TPSS (revTPSS) and the recently Balanced LOCalization (BLOC) meta-GGA of L.A. Constantin, E. Fabiano, and F. Della Sala, (J. Chem. Theory Comput. 9, 2256 (2013)). The empirical M06-L meta-GGA functional is also considered. Real-space analyses of atoms and ions as well as wave-vector analyses of jellium surface energies, show that the meta-GGA hole models, in particular the BLOC one, are very realistic and can reproduce many features of benchmark XC holes. In addition, the BLOC hole model can be used to estimate with good accuracy the Coulomb hole radius of small atoms and ions. Thus, the proposed meta-GGA hole models provide a valuable tool to validate in detail existing meta-GGA functionals, and can be further used in the development of DFT methods beyond the semilocal level of theory., Comment: 11 pages, 10 figures

We present a simple and non-empirical method to determine optimal scaling coefficients, within the (spin-component)-scaled MP2 approach, for calculating intermolecular potential energies of noncovalently-interacting systems. The method is based on an observed proportionality between (spin-component) MP2 and CCSD(T) energies for a wide range of intermolecular distances and allows to compute with high accuracy a large portion of the dissociation curve at the cost of a single CCSD(T) calculation. The accuracy of the present procedure is assessed for a series of noncovalently-interacting test systems: the obtained results reproduce CCSD(T) quality in all cases and definitely outperform conventional MP2, CCSD and SCS-MP2 results. The difficult case of the Beryllium dimer is also considered., Comment: 9 pages, 7 figures

We construct a meta-generalized-gradient approximation which properly balances the nonlocality contributions to the exchange and correlation at the semilocal level. This non-empirical functional shows good accuracy for a broad palette of properties (thermochemistry, structural properties) and systems (molecules, metal clusters, surfaces and bulk solids). The accuracy for several well known problems in electronic structure calculations, such as the bending potential of the silver trimer and the dimensional crossover of anionic gold clusters, is also demonstrated. The inclusion of empirical dispersion corrections is finally discussed and analyzed., Comment: 10 pages, 4 figures

We apply the frozen density embedding method, using a full relaxation of embedded densities through a freeze-and-thaw procedure, to study the electronic structure of several benchmark ground-state charge-transfer complexes, in order to assess the merits and limitations of the approach for this class of systems. The calculations are performed using both semilocal and hybrid exchange-correlation (XC) functionals. The results show that embedding calculations using semilocal XC functionals yield rather large deviations with respect to the corresponding supermolecular calculations. Due to a large error cancellation effect, however, they can often provide a relatively good description of the electronic structure of charge-transfer complexes, in contrast to supermolecular calculations performed at the same level of theory. On the contrary, when hybrid XC functionals are employed, both embedding and supermolecular calculations agree very well with each other and with the reference benchmark results. In conclusion, for the study of ground-state charge-transfer complexes via embedding calculations hybrid XC functionals are the method of choice due to their higher reliability and superior performance., Comment: 14 pages, 7 figures

We present a theoretical study of the ionization potential in small anionic gold clusters, using density functional theory, with and without exact-exchange, and many body perturbation theory, namely the G0W0 approach. We find that G0W0 is the best approach and correctly describes the first ionization potential with an accuracy of about 0.1 eV., Comment: 6 pages, 1 figure

We construct a reference benchmark set for atomic and molecular random-phase-approximation (RPA) correlation energies in a density functional theory (DFT) framework at the complete basis set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies accurate results, clearly outperforming raw data, are achievable with two-point extrapolation schemes based on quintuple- and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be also obtained by using a semiempirical extrapolation procedure based on quadruple- and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies., Comment: 10 pages, 2 figures

We discuss, simplify, and improve the spin-dependent correction of L.A. Constantin et al., Phys. Rev. B 84, 233103, for atomization energies, and develop a density parameter of the form $v\propto |\nabla n|/n^{10/9}$, found from the statistical ensemble of one-electron densities. The here constructed exchange-correlation generalized gradient approximations (GGAs), named zvPBEsol and zvPBEint, show a broad applicability, and a good accuracy for many applications, because these corrected functionals significantly improve the atomization and binding energies of molecular systems, without worsening the behavior of the original functionals (PBEsol and PBEint) for other properties. This spin-dependent correction is also applied to meta-GGA dynamical correlation functionals combined with exact-exchange; in this case a significant (about 30%) improvement in atomization energies of small molecules is found., Comment: 10 pages, 6 figures

We review the performance of the PBEint GGA functional (Phys. Rev. B 2010, 82, 113104) recently proposed to improve the description of hybrid interfaces, and we introduce its one-parameter hybrid form (hPBEint). We consider different well established benchmarks for energetic and structural properties of molecular and solid-state systems as well as model systems and newly developed benchmark sets for dipole moments and metal-molecule interactions. We find that PBEint and hPBEint (with 16.67% Hartree-Fock exchange) yield the overall best performance, working well for most of the considered properties and systems and showing a balanced behavior for different problems. In particular, due to their well-balanced accuracy, they perform well for the description of hybrid metal-molecule interfaces., Comment: 13 pages, 3 figures. Accepted for publication in Int. J. Quant. Chem. (2013), DOI: 10.1002/qua.24042

The High Density Effective Theory formalism is used to calculate the low energy properties of the phonons and gluons in the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of two-flavor QCD. The effective phonon Lagrangian for the cubic crystal structure, which is favored according to a recent study, depends, at the second order in the derivatives, on three parameters which we calculate in this paper. We also compute for soft momenta the effective lagrangian for the gluons of the unbroken SU(2)_c group, both for a single plane wave structure and for the cube. In both cases the Meissner gluon mass vanishes as in the case of complete isotropy; on the other hand there is a partial Debye screening due to the existence of blocking regions on the Fermi spheres. For the single plane wave structure the gluon dielectric tensor is non isotropic, while it is isotropic for the cubic crystal, in spite of the intrinsic anisotropy of the structure., Comment: 38 pages, 4 figures