Yuxiang Mo

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.

Assessment of the Tao-Mo nonempirical semilocal density functional in applications to 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 {\AA} 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.

Performance of a nonempirical density functional on molecules and hydrogen-bonded complexes

Recently, Tao and Mo 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 Tao-Mo functional can achieve high accuracy for most properties considered, relative to the local spin-density approximation, Perdew-Burke-Ernzerhof, and Tao-Perdew-Staroverov-Scuseria functionals. In particular, it yields the best accuracy for proton affinities, harmonic vibrational frequencies, hydrogen-bond dissociation energies and bond lengths, and atomic excitation energies.

Accurate excitation energies of molecules and oligomers from a semilocal density functional

Excitation energy plays an important role in energy conversion, biological processes, and optical devices. In this work, we apply the Tao-Mo (TM) nonempirical meta-generalized gradient approximation and the combination TMTPSS (TMx + TPSSc), with TPSSc being the correlation part of the original TPSS (Tao-Perdew-Staroverov-Scuseria) to study excitation energies of small molecules and oligomers. Our test set consists of 17 molecules with 134 total excited states, including singlet, triplet, valence, and Rydberg excited states. Our calculation shows that both the TMTPSS and TM functionals yield good overall performance, with mean absolute errors (MAEs) of 0.37 eV and 0.42 eV, respectively, outperforming commonly used semilocal functionals LSDA (MAE = 0.55 eV), PBE (MAE = 0.58 eV), and TPSS (MAE = 0.47 eV). In particular, TMTPSS can yield nearly the same accuracy of B3LYP (MAE = 0.36 eV), with lower computational cost. The accuracy for semilocal density functional theory continues to hold for conjugated oligomers, but they become less accurate than hybrid functionals, due to the insufficient nonlocality.

Energetic Study of Clusters and Reaction Barrier Heights from Efficient Semilocal Density Functionals

The accurate first-principles prediction of the energetic properties of molecules and clusters from efficient semilocal density functionals is of broad interest. Here we study the performance of a non-empirical Tao-Mo (TM) density functional on binding energies and excitation energies of titanium dioxide and water clusters, as well as reaction barrier heights. To make a comparison, a combination of the TM exchange part with the TPSS (Tao–Perdew–Staroverov–Scuseria) correlation functional—called TMTPSS—is also included in this study. Our calculations show that the best binding energies of titanium dioxide are predicted by PBE0 (Perdew–Burke–Ernzerhof hybrid functional), TM, and TMTPSS with nearly the same accuracy, while B3LYP (Beck’s three-parameter exchange part with Lee-Yang-Parr correlation), TPSS, and PBE (Perdew–Burke–Ernzerhof) yield larger mean absolute errors. For excitation energies of titanium and water clusters, PBE0 and B3LYP are the most accurate functionals, outperforming the performance of semilocal functionals due to the nonlocality problem suffered by the latter. Nevertheless, TMTPSS and TM functionals are still good accurate semilocal methods, improving upon the commonly-used TPSS and PBE functionals. We also find that the best reaction barrier heights are predicted by PBE0 and B3LYP, thanks to the nonlocality incorporated into these two hybrid functionals, but TMTPSS and TM are obviously more accurate than SCAN (Strongly Constrained and Appropriately Normed), TPSS, and PBE, suggesting the good performance of TM and TMTPSS for physically different systems and properties.

First-principles study of the binding energy between nanostructures and its scaling with system size

Jianmin Tao, ∗ Yang Jiao, Yuxiang Mo, Zeng-Hui Yang, Jian-Xin Zhu, Per Hyldgaard, and John P. Perdew Department of Physics, Temple University, Philadelphia, PA 19122-1801, USA Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, Sweden Microsystem and Terahertz Research Center, China Academy of Engineering Physics, Chengdu, Sichuan 610200, China Theoretical Division & Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA (Dated: October 11, 2018)