arXiv subjects

Jianmin Tao

Publications and source records attributed to Jianmin Tao.

At least 19 recordsLinked to original sources

arXiv2018

Origin of the size-dependence of the equilibrium van der Waals binding between nanostructures

Nanostructures can be bound together at equilibrium by the van der Waals (vdW) effect, a small but ubiquitous many-body attraction that presents challenges to density functional theory. How does the binding energy depend upon the size or number of atoms in one of a pair of identical nanostructures? To answer this question, we treat each nanostructure properly as a whole object, not as a collection of atoms. Our calculations start from an accurate static dipole polarizability for each considered nanostructure, and an accurate equilibrium center-to-center distance for the pair (the latter from experiment, or from the vdW-DF-cx functional). We consider the competition in each term $-C_{2k}/d^{2k}$ ($k=3, 4, 5$) of the long-range vdW series for the interaction energy, between the size dependence of the vdW coefficient $C_{2k}$ and that of the $2k$-th power of the center-to-center distance $d$. The damping of these vdW terms can be negligible, but in any case it does not affect the size dependence for a given term in the absence of non-vdW binding. To our surprise, the vdW energy can be size-independent for quasi-spherical nanoclusters bound to one another by vdW interaction, even with strong nonadditivity of the vdW coefficient, as demonstrated for fullerenes. We also show that, for low-dimensional systems, the vdW interaction yields the strongest size-dependence, in stark contrast to that of fullerenes. We illustrate this with parallel planar polycyclic aromatic hydrocarbons. Other cases are between, as shown by sodium clusters.

physics.chem-ph↗

arXiv2017

Energy scaling law for nanostructured materials

The equilibrium binding energy is an important factor in the design of materials and devices. However, it presents great computational challenges for materials built up from nanostructures. Here we investigate the binding-energy scaling law from first-principles calculations. We show that the equilibrium binding energy per atom between identical nanostructures can scale up or down with nanostructure size. From the energy scaling law, we predict finite large-size limits of binding energy per atom. We find that there are two competing factors in the determination of the binding energy: Nonadditivities of van der Waals coefficients and center-to-center distance between nanostructures. To uncode the detail, the nonadditivity of the static multipole polarizability is investigated. We find that the higher-order multipole polarizability displays ultra-strong intrinsic nonadditivity, no matter if the dipole polarizability is additive or not.

cond-mat.mes-hall↗

arXiv2016

Performance of a Nonempirical Density Functional on Molecules and Hydrogen-Bonded Complexes

Recently, Tao and Mo (TM) derived a meta-generalized gradient approximation functional based on a model exchange-correlation hole. In this work, the performance of this functional is assessed on standard test sets, using the 6-311++G(3df,3pd) basis set. These test sets include 223 G3/99 enthalpies of formation, 99 atomization energies, 76 barrier heights, 58 electron affinities, 8 proton affinities, 96 bond lengths, 82 harmonic vibrational frequencies, 10 hydrogen-bonded molecular complexes, and 22 atomic excitation energies. Our calculations show that the TM functional can achieve high accuracy for most properties considered, relative to the LSDA, PBE, and TPSS functionals. In particular, it yields the best accuracy for proton affinities, harmonic vibrational frequencies, hydrogen-bonded dissociation energies and bond lengths, and atomic excitation energies.

physics.chem-ph↗

arXiv2016

Comparative study of semilocal density functionals on solids and surfaces

Recently, Tao and Mo (TM) proposed an accurate all-purpose nonempirical meta-generalized gradient approximation (meta-GGA). The exchange part was derived from the density matrix approximation, while the correlation part is based on a modification of TPSS correlation in the low-density or strong-interaction limit. To further understand this density functional, we combine the TM exchange part with the original TPSS correlation and make a comprehensive assessment of this combination, which we call TMTPSS functional, on solids and solid surfaces. Our test includes 22 lattice constants and bulk moduli, 30 band gaps of semiconductors, 7 cohesive energies, and surface exchange-correlation energies for rs ranging from 2 to 3 bohr. Our calculations show that TMTPSS functional is quite competitive to the TM meta-GGA functional, improving upon the nonempirical functionals LSDA, PBE GGA, and TPSS meta-GGA for most properties considered. In particular, it significantly improves the surface exchange-correlation energy calculation, with a mean absolute error of only 1 erg/cm2.

cond-mat.mtrl-sci↗

arXiv2016

Performance of a nonempirical exchange functional from the density matrix expansion: comparative study with different correlation

Recently, Tao and Mo proposed an accurate meta-generalized gradient approximation for the exchange-correlation energy. The exchange part is derived from the density matrix expansion, while the correlation part is obtained by improving the TPSS correlation in the low-density limit. To better understand this exchange functional, in this work, we combine the TM exchange with the original TPSS correlation, which we call TMTPSS, and make a systematic assessment on molecular properties. The test sets include the 223 G3/99 enthalpies of formation, 58 electron affinities, 8 proton affinities, 96 bond lengths, 82 harmonic frequencies, and 10 hydrogen-bonded molecular complexes. Our calculations show that the TMTPSS functional is competitive with or even more accurate than TM functional for some properties. In particular, it is the most accurate nonempirical semilocal DFT for the enthalpies of formation and harmonic vibrational frequencies, suggesting the robustness of TM exchange.

physics.chem-ph↗

arXiv2016

Semilocal exchange hole with an application to range-separation density functional

Exchange-correlation hole is a central concept in density functional theory. It not only provides justification for an exchange-correlation energy functional, but also serves as a local ingredient in nonlocal range-separation density functional. However, due to the nonlocal nature, modelig the conventional exact exchange hole presents a great challenge to density functional theory. In this work, we propose a semilocal exchange hole underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional. The present model is distinct from previous models at small separation between an electron and the hole around the electron. It is also different in the way it interpolates between the rapidly varying iso-orbital density and the slowly varying density, which is determined by the wave vector analysis based on the exactly solvable infinite barrier model for jellium surface. Our numerical tests show that the exchange hole generated from this model mimics the conventional exact exchange hole quite well for atoms. Finally, as a simple application, we apply the hole model to construct a TPSS-based range-separation functional. Our tests show that this TPSS-based range-separation functional can substantially improve TPSS band gaps and barrier heights, without losing much accuracy of molecular atomization energies.

cond-mat.mtrl-sci↗

arXiv2016

Assessment of a nonempirical semilocal density functional on solids and surfaces

Recently, Tao and Mo developed a new nonempirical semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density matrix expansion corrected to reproduce the fourth-order gradient expansion in the slowly varying limit, while the correlation part is based on the TPSS correlation model with a modification for the low-density limit. In the present work, the Tao-Mo functional is assessed by calculations on a variety of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 7 cohesive energies, and jellium surface exchange and correlation energies for the density parameter rs in the range from 2 to 3 bohrs. Our calculations show that this meta-generalized gradient approximation can yield consistently remarkable accuracy for the properties considered here, with mean absolute errors of 0.017 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV for cohesive energies, and 35 erg/cm2 for surface exchange-correlation energies, substantially improving upon existing nonempirical semilocal density functionals.

cond-mat.mtrl-sci↗

arXiv2016

Accurate semilocal density functional for condensed matter physics and quantum chemistry

Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.

cond-mat.mtrl-sci↗

arXiv2016

Frequency-dependent dielectric function of semiconductors with application to physisorption

The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the long-range van der Waals (vdW) interaction for solids and adsorption. In this work, we calculate the frequency-dependent dielectric functions of semiconductors and insulators using the $GW$ method with and without exciton effects, as well as efficient semilocal density functional theory (DFT), and compare these calculations with a model frequency-dependent dielectric function. We find that for semiconductors with moderate band gaps, the model dielectric functions, $GW$ values, and DFT calculations all agree well with each other. However, for insulators with strong exciton effects, the model dielectric functions have a better agreement with accurate $GW$ values than the DFT calculations, particularly in high-frequency region. To understand this, we repeat the DFT calculations with scissors correction, by shifting DFT Kohn-Sham energy gap to match the experimental band gap. We find that scissors correction only moderately improves the DFT dielectric function in low-frequency region. Based on the dielectric functions calculated with different methods, we make a comparative study by applying these dielectric functions to calculate the vdW coefficients ($C_3$ and $C_5$) for adsorption of rare-gas atoms on a variety of surfaces. We find that the vdW coefficients obtained with the nearly-free electron gas-based model dielectric function agree quite well with those obtained from the $GW$ dielectric function, in particular for adsorption on semiconductors, leading to an overall error of less than 7% for $C_3$ and 5% for $C_5$. This demonstrates the reliability of the model dielectric function for the study of physisorption.

cond-mat.mtrl-sci↗

arXiv2012

Theory of ultrafast quasiparticle dynamics in high-temperature superconductors: Pump fluence dependence

We present a theory for the time-resolved optical spectroscopy of high-temperature superconductors at high excitation densities with strongly anisotropic electron-phonon coupling. A signature of the strong coupling between the out-of-plane, out-of-phase O buckling mode ($B_{1g}$) and electronic states near the antinode is observed as a higher-energy peak in the time-resolved optical conductivity and Raman spectra, while no evidence of the strong coupling between the in-plane Cu-O breathing mode and nodal electronic states is observed. More interestingly, it is observed that under appropriate conditions of pump fluence, this signature exhibits a re-entrant behavior with time delay, following the fate of the superconducting condensate.

cond-mat.supr-con↗

arXiv2010

Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integro-differential equation, whose only inputs are the one-particle density matrix and the pair correlation function of the ground-state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a hermitian eigenvalue problem, which admits a complete set of orthonormal eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle, and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.

cond-mat.other↗

arXiv2010

Theory of time-resolved spectral function in high-temperature superconductors with bosonic modes

We develop a three-temperature model to simulate the time dependence of electron and phonon temperatures in high-temperature superconductors displaying strong anistropic electron-phonon coupling. This model not only takes the tight-binding band structure into account, but also is valid in superconducting state. Based on this model, we calculate the time-resolved spectral function via the double-time Green's functions. We find that the dip-hump structure evolves with the time delay. More interestingly, new phononic structures are obtained when the phonons are excited by a laser field. This signature may serve as a direct evidence for electron-vibration mode coupling.

cond-mat.supr-con↗

arXiv2009

Can time-dependent density functional theory predict the excitation energies of conjugated polymers?

Excitation energies of light-emitting organic conjugated polymers have been investigated with time-dependent density functional theory (TDDFT) within the adiabatic approximation for the dynamical exchange-correlation potential. Our calculations show that the accuracy of the calculated TDDFT excitation energies largely depends upon the accuracy of the dihedral angle obtained by the geometry optimization on ground-state DFT methods. We find that, when the DFT torsional dihedral angles between two adjacent phenyl rings are close to the experimental dihedral angles, the TDDFT excitation energies agree fairly well with experimental values. Further study shows that, while hybrid density functionals can correctly respect the thumb rule between singlet-singlet and singlet-triplet excitation energies, semilocal functionals do not, suggesting inadequacy of the semilocal functionals in predicting triplet excitation energies of conjugated polymers.

cond-mat.mtrl-sci↗

arXiv2009

Linear Continuum Mechanics for Quantum Many-Body Systems

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.

cond-mat.str-el↗

arXiv2008

Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction

We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. "Normal" regions are well described by semilocal approximations, because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. "Abnormal" regions, where nonlocality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semilocal exchange energy densities locally. Because our mixing fraction tends to 1 in the high-density limit, we rigorously employ full exact exchange. However, the nonlocality of exchange also requires balanced nonlocality of correlation, which can demand at least five empirical parameters. Our local hybrid functional is perhaps the first size-consistent fourth-rung density functional or hyper-GGA with full exact exchange, is exact for all one-electron densities, and provides an excellent fit to the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids.

physics.chem-ph↗

arXiv2008

Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response

Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS) nonempirical meta-generalized gradient approximation (meta-GGA) for the exchange-correlation energy yields more accurate surface energies than the local spin density (LSD) approximation for spin-unpolarized jellium. In this study, work functions and surface energies of a jellium metal in the presence of ``internal'' and external magnetic fields are calculated with LSD, Perdew-Burke-Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the nearly nonempirical Perdew-Kurth-Zupan-Blaha (PKZB) meta-GGA, using self-consistent LSD orbitals and densities. The results show that: (i) For normal bulk densities, the surface correlation energy is the same in TPSS as in PBE, as it should be since TPSS strives to represent a self-correlation correction to PBE; (ii) Normal surface density profiles can be scaled uniformly to the low-density or strong-interaction limit, and TPSS provides an estimate for that limit that is consistent with (but probably more accurate than) other estimates; (iii) For both normal and low densities, TPSS provides the same description of surface magnetism as PBE, suggesting that these approximations may be generally equivalent for magnetism. The energies of jellium spheres with up to 106 electrons are calculated using density functionals and compared to those obtained with Diffusion Quantum Monte Carlo data, including our estimate for the fixed-node correction. Finally we calculate the linear response of bulk jellium using these density functionals, and find that not only LSD but also PBE GGA and TPSS meta-GGA yield a linear-response in good agreement with that of the Quantum Monte Carlo method, for wavevectors of the perturbing external potential up to twice the Fermi wavevector.

cond-mat.mtrl-sci↗

arXiv2008

Quantum Stress Focusing in Descriptive Chemistry

We show that several important concepts of descriptive chemistry, such as atomic shells, bonding electron pairs and lone electron pairs, may be described in terms of {\it quantum stress focusing}, i.e. the spontaneous formation of high-pressure regions in an electron gas. This description subsumes previous mathematical constructions, such as the Laplacian of the density and the electron localization function, and provides a new tool for visualizing chemical structure. We also show that the full stress tensor, defined as the derivative of the energy with respect to a local deformation, can be easily calculated from density functional theory.

cond-mat.mtrl-sci↗

arXiv2007

Exact-exchange energy density in the gauge of a semilocal density functional approximation

Exact-exchange energy density and energy density of a semilocal density functional approximation are two key ingredients for modeling the static correlation, a strongly nonlocal functional of the density, through a local hybrid functional. Because energy densities are not uniquely defined, the conventional (Slater) exact-exchange energy density $e_\mathrm{x}^\mathrm{ex(conv)}$ is not necessarily well-suited for local mixing with a given semilocal approximation. We show how to transform $e_\mathrm{x}^\mathrm{ex(conv)}$ in order to make it compatible with an arbitrary semilocal density functional, taking the nonempirical meta-generalized gradient approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS) as an example. Our additive gauge transformation function integrates to zero, satisfies exact constraints, and is most important where the density is dominated by a single orbital shape. We show that, as expected, the difference between semilocal and exact-exchange energy densities becomes more negative under bond stretching in He$_2^{+}$ and related systems. Our construction of $e_\mathrm{x}^\mathrm{ex(conv)}$ by a resolution-of-the-identity method requires uncontracted basis functions.

cond-mat.mtrl-sci↗